Acta Applicandae Mathematicae, ISSN 0167-8019, 12/2010, Volume 112, Issue 3, pp. 323 - 346

The Hosoya index and the Merrifield-Simmons index are typical examples of graph invariants used in mathematical chemistry for quantifying relevant details of...

Theoretical, Mathematical and Computational Physics | Mathematics | 05C70 | Statistical Physics, Dynamical Systems and Complexity | 92E10 | Hosoya index | Merrifield-Simmons index | Mechanics | Mathematics, general | Molecular graphs | Computer Science, general | Extremal problem | 05C35 | MATHEMATICS, APPLIED | THERMODYNAMIC PROPERTIES | K-INDEPENDENT SETS | PI-ELECTRONIC SYSTEMS | TOPOLOGICAL INDEX | FIBONACCI NUMBERS | DOUBLE HEXAGONAL CHAINS | EXTREMAL UNICYCLIC GRAPHS | PRESCRIBED PENDENT VERTICES | ACYCLIC SATURATED-HYDROCARBONS | Surveys | Methods | Universities and colleges | Studies | Chemistry | Graph theory | Molecular structure | Mathematical analysis

Theoretical, Mathematical and Computational Physics | Mathematics | 05C70 | Statistical Physics, Dynamical Systems and Complexity | 92E10 | Hosoya index | Merrifield-Simmons index | Mechanics | Mathematics, general | Molecular graphs | Computer Science, general | Extremal problem | 05C35 | MATHEMATICS, APPLIED | THERMODYNAMIC PROPERTIES | K-INDEPENDENT SETS | PI-ELECTRONIC SYSTEMS | TOPOLOGICAL INDEX | FIBONACCI NUMBERS | DOUBLE HEXAGONAL CHAINS | EXTREMAL UNICYCLIC GRAPHS | PRESCRIBED PENDENT VERTICES | ACYCLIC SATURATED-HYDROCARBONS | Surveys | Methods | Universities and colleges | Studies | Chemistry | Graph theory | Molecular structure | Mathematical analysis

Journal Article

Croatica Chemica Acta, ISSN 0011-1643, 12/2013, Volume 86, Issue 4, pp. 351 - 361

The degree of a vertex of a molecular graph is the number of first neighbors of this vertex. A large number of molecular-graph-based structure descriptors...

Vertex-degree-based topological index | Topological index | Chemical graph theory | Molecular graph | Molecular structure descriptor | molecular structure descriptor | BENZENOID SYSTEMS | GEOMETRIC-ARITHMETIC INDEX | ABC INDEX | ATOM-BOND CONNECTIVITY | MOLECULAR CONNECTIVITY | CHEMISTRY, MULTIDISCIPLINARY | topological index | COORDINATION-COMPOUNDS | vertex-degree-based topological index | UNIFIED APPROACH | VARIABLE ZAGREB INDEXES | molecular graph | chemical graph theory | GENERAL RANDIC INDEX | UNICYCLIC GRAPHS | Graph theory | Research | Topology | Mathematical research | Algebraic topology | Graphs | Molecular chemistry

Vertex-degree-based topological index | Topological index | Chemical graph theory | Molecular graph | Molecular structure descriptor | molecular structure descriptor | BENZENOID SYSTEMS | GEOMETRIC-ARITHMETIC INDEX | ABC INDEX | ATOM-BOND CONNECTIVITY | MOLECULAR CONNECTIVITY | CHEMISTRY, MULTIDISCIPLINARY | topological index | COORDINATION-COMPOUNDS | vertex-degree-based topological index | UNIFIED APPROACH | VARIABLE ZAGREB INDEXES | molecular graph | chemical graph theory | GENERAL RANDIC INDEX | UNICYCLIC GRAPHS | Graph theory | Research | Topology | Mathematical research | Algebraic topology | Graphs | Molecular chemistry

Journal Article

MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, ISSN 0340-6253, 2017, Volume 78, Issue 1, pp. 17 - 100

Let G be a graph with vertex set V(G) and edge set E(G). Let d(i) be the degree of the vertex v(i) is an element of V(G). The first and second Zagreb indices,...

PENDENT VERTICES | EXTREMAL GRAPHS | CHEMISTRY, MULTIDISCIPLINARY | SHARP UPPER-BOUNDS | INDEPENDENCE NUMBER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOLECULAR-ORBITALS | DEGREE SEQUENCES | CONNECTED GRAPHS | UNICYCLIC GRAPHS | TOPOLOGICAL INDEXES | BIPARTITE GRAPHS

PENDENT VERTICES | EXTREMAL GRAPHS | CHEMISTRY, MULTIDISCIPLINARY | SHARP UPPER-BOUNDS | INDEPENDENCE NUMBER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOLECULAR-ORBITALS | DEGREE SEQUENCES | CONNECTED GRAPHS | UNICYCLIC GRAPHS | TOPOLOGICAL INDEXES | BIPARTITE GRAPHS

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 2015, Volume 53, Issue 4, pp. 1184 - 1190

In 1972, within a study of the structure-dependency of total -electron energy (), it was shown that depends on the sum of squares of the vertex degrees of the...

Zagreb index | Topological index | Forgotten index | First Zagreb index | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOLECULAR-ORBITALS | GRAPH-THEORY | CHEMISTRY, MULTIDISCIPLINARY

Zagreb index | Topological index | Forgotten index | First Zagreb index | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOLECULAR-ORBITALS | GRAPH-THEORY | CHEMISTRY, MULTIDISCIPLINARY

Journal Article

1996, Memoirs of the American Mathematical Society, ISBN 0821804405, Volume no. 571., vii, 184

Book

Applied Mathematics and Computation, ISSN 0096-3003, 08/2014, Volume 240, pp. 213 - 228

There are certain types of topological indices such as degree based topological indices, distance based topological indices and counting related topological...

Silicate network | ABC index | Hexagonal network | Topological index | Honeycomb network | Oxide network | MATHEMATICS, APPLIED | CONNECTIVITY INDEX | Silicates | Chemical properties | Networks | Computation | Chains | Oxides | Topology | Chemical compounds | Counting

Silicate network | ABC index | Hexagonal network | Topological index | Honeycomb network | Oxide network | MATHEMATICS, APPLIED | CONNECTIVITY INDEX | Silicates | Chemical properties | Networks | Computation | Chains | Oxides | Topology | Chemical compounds | Counting

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 12/2014, Volume 178, pp. 83 - 88

The classical first and second Zagreb indices of a graph are defined as and , where is the degree of the vertex of . So far, the difference of and has not been...

Zagreb index | Degree (of vertex) | Second Zagreb index | First Zagreb index | MATHEMATICS, APPLIED | MOLECULAR-ORBITALS | INEQUALITY | SUM | SQUARES | GRAPH-THEORY | TOPOLOGICAL INDEXES

Zagreb index | Degree (of vertex) | Second Zagreb index | First Zagreb index | MATHEMATICS, APPLIED | MOLECULAR-ORBITALS | INEQUALITY | SUM | SQUARES | GRAPH-THEORY | TOPOLOGICAL INDEXES

Journal Article

MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, ISSN 0340-6253, 2018, Volume 79, Issue 1, pp. 5 - 54

Based on the definition of the general geometric-arithmetic index, this article introduces several new geometric-arithmetic indices (Part One). In Part Three,...

GRAPH | ALCOHOLS | COMBUSTION | QSPR | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | HEATS | ACIDS | VERSION | CHEMISTRY, MULTIDISCIPLINARY | TOPOLOGICAL INDEXES

GRAPH | ALCOHOLS | COMBUSTION | QSPR | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | HEATS | ACIDS | VERSION | CHEMISTRY, MULTIDISCIPLINARY | TOPOLOGICAL INDEXES

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 05/2013, Volume 219, Issue 17, pp. 8973 - 8978

One of the general requirements for any topological index is that similar molecules have near-lying -values, which is referred to as “smoothness”. Curiously,...

Graphs | Topological indices | Structural graph analysis | MATHEMATICS, APPLIED | 1ST | BOUNDS | ATOM-BOND CONNECTIVITY | DESCRIPTORS | AUGMENTED ZAGREB INDEX | ALKANES | Trees | Titanium | Mathematical models | Topology | Computation | Smoothness

Graphs | Topological indices | Structural graph analysis | MATHEMATICS, APPLIED | 1ST | BOUNDS | ATOM-BOND CONNECTIVITY | DESCRIPTORS | AUGMENTED ZAGREB INDEX | ALKANES | Trees | Titanium | Mathematical models | Topology | Computation | Smoothness

Journal Article

Computational Materials Science, ISSN 0927-0256, 03/2015, Volume 99, pp. 73 - 80

Nanoclusters create the possibility of designing novel properties and devices based on finite structures, with small dimensions. Clusters are of interest for...

Nanocluster | Gold | Topological index | Platinum | Asymptotic limits | WIENER INDEXES | MATERIALS SCIENCE, MULTIDISCIPLINARY | NANOCRYSTALS | ALGORITHM | INFINITE FAMILY | NANOSTRUCTURES | DISTANCE MATRIX | KIRCHHOFF | FULLERENES | CLUSTERS | SZEGED INDEX | Asymptotic properties | Mathematical analysis | Clusters | Mathematical models | Nanostructure | Topology | Atomic structure | Devices | Power law

Nanocluster | Gold | Topological index | Platinum | Asymptotic limits | WIENER INDEXES | MATERIALS SCIENCE, MULTIDISCIPLINARY | NANOCRYSTALS | ALGORITHM | INFINITE FAMILY | NANOSTRUCTURES | DISTANCE MATRIX | KIRCHHOFF | FULLERENES | CLUSTERS | SZEGED INDEX | Asymptotic properties | Mathematical analysis | Clusters | Mathematical models | Nanostructure | Topology | Atomic structure | Devices | Power law

Journal Article

Croatica Chemica Acta, ISSN 0011-1643, 06/2003, Volume 76, Issue 2, pp. 113 - 124

The original formulation of the Zagreb indices is presented and their relationship to topological indices such as self-returning walks, Platt,...

Connectivity indices | Zagreb indices | Molecular graphs | QSPR | VERTEX-CONNECTIVITY INDEX | NEURAL NETWORKS | HYDROCARBONS | COMPLEMENT-INHIBITORY ACTIVITY | MOLECULAR CONNECTIVITY | GRAPH-THEORY | DESCRIPTORS | CHEMISTRY, MULTIDISCIPLINARY | connectivity indices | QSAR | molecular graphs | BOILING POINTS | TOPOLOGICAL INDEXES

Connectivity indices | Zagreb indices | Molecular graphs | QSPR | VERTEX-CONNECTIVITY INDEX | NEURAL NETWORKS | HYDROCARBONS | COMPLEMENT-INHIBITORY ACTIVITY | MOLECULAR CONNECTIVITY | GRAPH-THEORY | DESCRIPTORS | CHEMISTRY, MULTIDISCIPLINARY | connectivity indices | QSAR | molecular graphs | BOILING POINTS | TOPOLOGICAL INDEXES

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2015, Volume 270, pp. 142 - 147

Let , and be, respectively, the Wiener, Szeged, PI, and Wiener polarity indices of a molecular graph . Let and be the first and second Zagreb indices of . We...

Zagreb index | Distance–based indices | Degree–based indices | Wiener index | Topological index | Szeged index | Degree-based indices | Distance-based indices | MATHEMATICS, APPLIED | NUMBER | ENERGY | WIENER POLARITY INDEX | GRAPH-THEORY | TREES | DIFFERENCE | MOLECULAR-ORBITALS | 1ST ZAGREB INDEX | VERTICES

Zagreb index | Distance–based indices | Degree–based indices | Wiener index | Topological index | Szeged index | Degree-based indices | Distance-based indices | MATHEMATICS, APPLIED | NUMBER | ENERGY | WIENER POLARITY INDEX | GRAPH-THEORY | TREES | DIFFERENCE | MOLECULAR-ORBITALS | 1ST ZAGREB INDEX | VERTICES

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 02/2019, Volume 57, Issue 2, pp. 609 - 615

The inverse problem for integer-valued topological indices is about the existence of a graph having its index value equal to a given integer. We solve this...

Zagreb index | Hyper-Zagreb index | Forgotten index | Second Zagreb index | First Zagreb index | Secondary 05C90 | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Primary 05C09 | CHEMISTRY, MULTIDISCIPLINARY | TOPOLOGICAL INDEXES | Trees | Graphs | Inverse problems

Zagreb index | Hyper-Zagreb index | Forgotten index | Second Zagreb index | First Zagreb index | Secondary 05C90 | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Primary 05C09 | CHEMISTRY, MULTIDISCIPLINARY | TOPOLOGICAL INDEXES | Trees | Graphs | Inverse problems

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2015, Volume 268, pp. 1259 - 1266

Mathematical properties of many topological indices are investigated. Knor et al. gave an upper bound for the Balaban index of -regular graphs on vertices and...

The (revised) Szeged index | Fullerene graph | Sum-Balaban index | Regular graph | CONNECTIVE ECCENTRICITY INDEX | MATHEMATICS, APPLIED | BICYCLIC GRAPHS | WIENER POLARITY INDEX | 1ST ZAGREB INDEX | TRICYCLIC GRAPHS | GENERAL RANDIC INDEX | UNICYCLIC GRAPHS | COMMON NEIGHBORHOOD GRAPHS | MOLECULAR GRAPHS | TOPOLOGICAL INDEXES

The (revised) Szeged index | Fullerene graph | Sum-Balaban index | Regular graph | CONNECTIVE ECCENTRICITY INDEX | MATHEMATICS, APPLIED | BICYCLIC GRAPHS | WIENER POLARITY INDEX | 1ST ZAGREB INDEX | TRICYCLIC GRAPHS | GENERAL RANDIC INDEX | UNICYCLIC GRAPHS | COMMON NEIGHBORHOOD GRAPHS | MOLECULAR GRAPHS | TOPOLOGICAL INDEXES

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 01/2019, Volume 42, Issue 1, pp. 67 - 78

For a graph G=(V(G),E(G)), let d(u),d(v) be the degrees of the vertices u,v in G. The first and second Zagreb indices of G are defined as M1(G)=Sigma...

Zagreb index | Multiplicative Zagreb index | Eulerian graphs | Extremal bounds | MATHEMATICS | ENERGY | EXTREMAL VALUES | CACTI | MOLECULAR-ORBITALS | SHARP BOUNDS | TOPOLOGICAL INDEXES | BIPARTITE GRAPHS | Organic chemistry | Computational chemistry | Graphs | Apexes

Zagreb index | Multiplicative Zagreb index | Eulerian graphs | Extremal bounds | MATHEMATICS | ENERGY | EXTREMAL VALUES | CACTI | MOLECULAR-ORBITALS | SHARP BOUNDS | TOPOLOGICAL INDEXES | BIPARTITE GRAPHS | Organic chemistry | Computational chemistry | Graphs | Apexes

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 8/2016, Volume 32, Issue 2, pp. 550 - 562

The Hosoya index $$m(G)$$ m ( G ) and the Merrifield–Simmons index $$i(G)$$ i ( G ) of a graph $$G$$ G are the number of matchings and the number of...

05C12 | 05D40 | 05C90 | Mathematics | Theory of Computation | 05C80 | Optimization | Expected value | Convex and Discrete Geometry | Hosoya index | Merrifield–Simmon index | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Polyphenylene chain | MATHEMATICS, APPLIED | THERMODYNAMIC PROPERTIES | ENERGY | HEXAGONAL CHAINS | ENUMERATION | PI-ELECTRONIC SYSTEMS | Merrifield-Simmon index | TOPOLOGICAL INDEX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SENSITIVE GRAPHICAL SUBSETS | ACYCLIC SATURATED-HYDROCARBONS | SPIRO | ALKANES

05C12 | 05D40 | 05C90 | Mathematics | Theory of Computation | 05C80 | Optimization | Expected value | Convex and Discrete Geometry | Hosoya index | Merrifield–Simmon index | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Polyphenylene chain | MATHEMATICS, APPLIED | THERMODYNAMIC PROPERTIES | ENERGY | HEXAGONAL CHAINS | ENUMERATION | PI-ELECTRONIC SYSTEMS | Merrifield-Simmon index | TOPOLOGICAL INDEX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SENSITIVE GRAPHICAL SUBSETS | ACYCLIC SATURATED-HYDROCARBONS | SPIRO | ALKANES

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 06/2017, Volume 302, pp. 111 - 121

The general Randić index of a graph is defined as where ( ) denotes the degree of a vertex in and is a real number. In this paper, we determine the maximum...

Chemical tree | Tree | Randić index | General Randić index | MATHEMATICS, APPLIED | Randic index | General Randic index | GEOMETRIC-ARITHMETIC INDEX | FIXED NUMBER | BICYCLIC GRAPHS | SUM-CONNECTIVITY INDEX | CHEMICAL TREES | WIENER INDEX | ZAGREB INDEXES | HARARY INDEX | UNICYCLIC GRAPHS | TOPOLOGICAL INDEXES

Chemical tree | Tree | Randić index | General Randić index | MATHEMATICS, APPLIED | Randic index | General Randic index | GEOMETRIC-ARITHMETIC INDEX | FIXED NUMBER | BICYCLIC GRAPHS | SUM-CONNECTIVITY INDEX | CHEMICAL TREES | WIENER INDEX | ZAGREB INDEXES | HARARY INDEX | UNICYCLIC GRAPHS | TOPOLOGICAL INDEXES

Journal Article

Amino Acids, ISSN 0939-4451, 8/2019, Volume 51, Issue 8, pp. 1209 - 1220

Up to now, numerous peptides/hydrolysates derived from casein and whey protein have shown angiotensin-I-converting enzyme (ACE) inhibitory. In this research,...

Biochemistry, general | Quantum topological molecular similarity | Neurobiology | Life Sciences | Auto cross covariance | Analytical Chemistry | Angiotensin-I-converting enzyme (ACE) | Amino acid index | Life Sciences, general | Biochemical Engineering | Proteomics | Quantitative sequence activity modeling | Peptide | REGRESSION | PRINCIPAL COMPONENT ANALYSIS | QSAR MODELS | STRATEGY | BIOCHEMISTRY & MOLECULAR BIOLOGY | SOLUBILITY | PROTEINS | TOOLS | Chymotrypsin | Goats | Casein | Analysis | Resveratrol | Angiotensin | Amino acids | Milk | Peptides | Whey | Hydrolysates | Proteins | Trypsin | Covariance | Sheep | Modelling | Whey protein | Index Medicus

Biochemistry, general | Quantum topological molecular similarity | Neurobiology | Life Sciences | Auto cross covariance | Analytical Chemistry | Angiotensin-I-converting enzyme (ACE) | Amino acid index | Life Sciences, general | Biochemical Engineering | Proteomics | Quantitative sequence activity modeling | Peptide | REGRESSION | PRINCIPAL COMPONENT ANALYSIS | QSAR MODELS | STRATEGY | BIOCHEMISTRY & MOLECULAR BIOLOGY | SOLUBILITY | PROTEINS | TOOLS | Chymotrypsin | Goats | Casein | Analysis | Resveratrol | Angiotensin | Amino acids | Milk | Peptides | Whey | Hydrolysates | Proteins | Trypsin | Covariance | Sheep | Modelling | Whey protein | Index Medicus

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 07/2017, Volume 1863, Issue 1

In this paper, we study with some graph descriptors also called topological indices. These descriptors are useful in determination of some properties of...

Zagreb Indices | Graph | Topological Index | Graph Descriptor | Organic chemistry

Zagreb Indices | Graph | Topological Index | Graph Descriptor | Organic chemistry

Journal Article