Graphs and Combinatorics, ISSN 0911-0119, 7/2014, Volume 30, Issue 4, pp. 977 - 1002

Extending the work of Godsil and others, we investigate the notion of the inverse of a graph...

Transitive closure | Unicyclic graph | Unique perfect matching | Inverse graph | Mathematics | Engineering Design | Combinatorics | Digraph | MATHEMATICS | Graphs | Matching | Construction | Inverse | Graph theory | Criteria | Combinatorial analysis

Transitive closure | Unicyclic graph | Unique perfect matching | Inverse graph | Mathematics | Engineering Design | Combinatorics | Digraph | MATHEMATICS | Graphs | Matching | Construction | Inverse | Graph theory | Criteria | Combinatorial 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...

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

Discrete Applied Mathematics, ISSN 0166-218X, 2011, Volume 159, Issue 15, pp. 1617 - 1630

The atom–bond connectivity (ABC) index of a graph G is defined as A B C ( G ) = ∑ u v ∈ E ( G ) d u + d v − 2 d u d v , where E...

Bicyclic graphs | Atom–bond connectivity index | Extremal graphs | Maximum degree | Unicyclic graphs | Pendent vertices | Atombond connectivity index | MATHEMATICS, APPLIED | Atom-bond connectivity index | ALKANES | Graphs | Mathematical analysis | Upper bounds | Images

Bicyclic graphs | Atom–bond connectivity index | Extremal graphs | Maximum degree | Unicyclic graphs | Pendent vertices | Atombond connectivity index | MATHEMATICS, APPLIED | Atom-bond connectivity index | ALKANES | Graphs | Mathematical analysis | Upper bounds | Images

Journal Article

Match, ISSN 0340-6253, 2014, Volume 71, Issue 3, pp. 461 - 508

This survey outlines results on graphs extremal with respect to distance-based indices, with emphasis on the Wiener index, hyper-Wiener index, Harary index, Wiener polarity index, reciprocal...

POLARITY INDEX | HYPER-WIENER INDEX | BICYCLIC GRAPHS | CHEMISTRY, MULTIDISCIPLINARY | AVERAGE DISTANCE | MEAN DISTANCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOLECULAR-ORBITALS | HARARY INDEX | 7 SMALLEST | UNICYCLIC GRAPHS | GUTMAN TREES

POLARITY INDEX | HYPER-WIENER INDEX | BICYCLIC GRAPHS | CHEMISTRY, MULTIDISCIPLINARY | AVERAGE DISTANCE | MEAN DISTANCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOLECULAR-ORBITALS | HARARY INDEX | 7 SMALLEST | UNICYCLIC GRAPHS | GUTMAN TREES

Journal Article

Match, ISSN 0340-6253, 2008, Volume 60, Issue 2, pp. 461 - 472

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy E-D(G...

MATRIX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MINIMAL ENERGY | UNICYCLIC GRAPHS | CHEMISTRY, MULTIDISCIPLINARY

MATRIX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MINIMAL ENERGY | UNICYCLIC GRAPHS | CHEMISTRY, MULTIDISCIPLINARY

Journal Article

数学学报：英文版, ISSN 1439-8516, 2016, Volume 32, Issue 12, pp. 1477 - 1493

In this paper, for the purpose of measuring the non-self-centrality extent of non-self- centered graphs, a novel eccerttricity-based invariant, named as non-self-centrality number...

third Zagreb eccentricity index | 05C12 | Eccentricity | diameter | non-self-centrality number | non-self-centered graph | Mathematics, general | Mathematics | 05C35 | MATHEMATICS, APPLIED | SUM | DEGREE DISTANCE | COMPARING ZAGREB INDEXES | MATHEMATICS | TREES | WIENER INDEX | CONNECTED GRAPHS | HARARY INDEXES | UNICYCLIC GRAPHS | Studies | Graphs | Theorems | Mathematical models | Applied mathematics | Upper bounds | Texts | Graph theory | Formulas (mathematics) | Invariants

third Zagreb eccentricity index | 05C12 | Eccentricity | diameter | non-self-centrality number | non-self-centered graph | Mathematics, general | Mathematics | 05C35 | MATHEMATICS, APPLIED | SUM | DEGREE DISTANCE | COMPARING ZAGREB INDEXES | MATHEMATICS | TREES | WIENER INDEX | CONNECTED GRAPHS | HARARY INDEXES | UNICYCLIC GRAPHS | Studies | Graphs | Theorems | Mathematical models | Applied mathematics | Upper bounds | Texts | Graph theory | Formulas (mathematics) | Invariants

Journal Article

Match, ISSN 0340-6253, 2008, Volume 59, Issue 1, pp. 5 - 124

KEKULE VALENCE STRUCTURES | SYMMETRY PROPERTIES | MOLECULAR CONNECTIVITY | CHEMISTRY, MULTIDISCIPLINARY | PROPERTY-ACTIVITY REGRESSIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | RESONANCE ENERGIES | VARIABLE CONNECTIVITY INDEX | THEORETICAL APPROACH | 2 UNSOLVED QUESTIONS | UNICYCLIC GRAPHS | ELECTRONIC-STRUCTURE

Journal Article

PLoS ONE, ISSN 1932-6203, 06/2015, Volume 10, Issue 6, p. e0129497

For a given graph G, epsilon(v) and deg(v) denote the eccentricity and the degree of the vertex v in G, respectively...

MAXIMAL ENERGY | CONNECTIVITY INDEX | ANTI-HIV ACTIVITY | MULTIDISCIPLINARY SCIENCES | COMPUTATIONAL APPROACH | TRICYCLIC GRAPHS | WIENER POLARITY INDEX | GENERAL RANDIC INDEX | UNICYCLIC GRAPHS | TOPOLOGICAL DESCRIPTOR | INCIDENCE ENERGY | Models, Theoretical | Algorithms | Antioxidants | Connectivity | Chemistry | Energy | Eccentricity | Biological activity

MAXIMAL ENERGY | CONNECTIVITY INDEX | ANTI-HIV ACTIVITY | MULTIDISCIPLINARY SCIENCES | COMPUTATIONAL APPROACH | TRICYCLIC GRAPHS | WIENER POLARITY INDEX | GENERAL RANDIC INDEX | UNICYCLIC GRAPHS | TOPOLOGICAL DESCRIPTOR | INCIDENCE ENERGY | Models, Theoretical | Algorithms | Antioxidants | Connectivity | Chemistry | Energy | Eccentricity | Biological activity

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2016, Volume 433, Issue 2, pp. 803 - 817

The connective eccentricity index (CEI) of a graph G is defined as ξce(G)=∑vi∈V(G)d(vi)ε(vi) where ε(vi) and d(vi) are the eccentricity and the degree of vertex vi, respectively, in G...

Tree | Connective eccentricity index | Eccentric connectivity index | Extremal graph | Matching number | MATHEMATICS, APPLIED | SUM | DEGREE DISTANCE | TOPOLOGICAL DESCRIPTOR | MATHEMATICS | TREES | ZAGREB INDEXES | UNICYCLIC GRAPHS

Tree | Connective eccentricity index | Eccentric connectivity index | Extremal graph | Matching number | MATHEMATICS, APPLIED | SUM | DEGREE DISTANCE | TOPOLOGICAL DESCRIPTOR | MATHEMATICS | TREES | ZAGREB INDEXES | UNICYCLIC GRAPHS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2016, Volume 289, pp. 464 - 480

The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph...

Kirchhoff index | Unicyclic graph | Resistance distance | Matching number | WIENER INDEXES | MATHEMATICS, APPLIED | ENERGY-LIKE INVARIANT | TREES | BOUNDS | RESISTANCE-DISTANCE | Information science | Statistics

Kirchhoff index | Unicyclic graph | Resistance distance | Matching number | WIENER INDEXES | MATHEMATICS, APPLIED | ENERGY-LIKE INVARIANT | TREES | BOUNDS | RESISTANCE-DISTANCE | Information science | Statistics

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 11/2014, Volume 30, Issue 6, pp. 1551 - 1563

Let G = (V, E) be a connected graph. The hamiltonian index h(G) (Hamilton-connected index hc(G...

Hamilton-connected index | Unicyclic graph | 05C45 | Spanning connectivity | 05C40 | Hamiltonian index | Power of graph | Tree | Mathematics | Engineering Design | Combinatorics | SHORT PROOF | SQUARE | FLEISCHNERS THEOREM | BLOCK | CUBE | MATHEMATICS | ITERATED LINE GRAPHS | CYCLES | Graph representations | Graphs | Integers | Trees | Combinatorial analysis

Hamilton-connected index | Unicyclic graph | 05C45 | Spanning connectivity | 05C40 | Hamiltonian index | Power of graph | Tree | Mathematics | Engineering Design | Combinatorics | SHORT PROOF | SQUARE | FLEISCHNERS THEOREM | BLOCK | CUBE | MATHEMATICS | ITERATED LINE GRAPHS | CYCLES | Graph representations | Graphs | Integers | Trees | Combinatorial analysis

Journal Article

12.
Full Text
Spectral radius and extremal graphs for class of unicyclic graph with pendant vertices

Advances in Mechanical Engineering, ISSN 1687-8132, 7/2017, Volume 9, Issue 7, p. 168781401770713

In this article, we research on the spectral radius of extremal graphs for the unicyclic graphs with girth g mainly by the graft transformation and matching and obtain the upper bounds of the spectral...

graft transformation | Unicyclic graph | spectral radius | matching | THERMODYNAMICS | ENGINEERING, MECHANICAL | Studies | Input output | Researchers | Upper bounds | Graphs | Spectra | Graph theory | Eigen values

graft transformation | Unicyclic graph | spectral radius | matching | THERMODYNAMICS | ENGINEERING, MECHANICAL | Studies | Input output | Researchers | Upper bounds | Graphs | Spectra | Graph theory | Eigen values

Journal Article

Applicable analysis and discrete mathematics, ISSN 1452-8630, 10/2017, Volume 11, Issue 2, pp. 273 - 298

We present a linear time algorithm that computes the number of eigenvalues of a unicyclic graph in a given real interval...

Zero | Algorithms | Plant roots | Eigenvalues | Caterpillars | Scalars | Laplacians | Spectral graph theory | Diagonal arguments | Vertices | Closed caterpillars | Localization of eigenvalues | Unicyclic graphs | localization of eigenvalues | MATHEMATICS | MATHEMATICS, APPLIED | TREES | closed caterpillars | LAPLACIAN EIGENVALUES

Zero | Algorithms | Plant roots | Eigenvalues | Caterpillars | Scalars | Laplacians | Spectral graph theory | Diagonal arguments | Vertices | Closed caterpillars | Localization of eigenvalues | Unicyclic graphs | localization of eigenvalues | MATHEMATICS | MATHEMATICS, APPLIED | TREES | closed caterpillars | LAPLACIAN EIGENVALUES

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2019, Volume 39, Issue 2, pp. 489 - 503

For ≥ 1, a -fair dominating set (or just FD-set) in a graph is a dominating set such that | ) ∩ | = for every vertex ∈ \ . The -fair domination number of , denoted...

fair domination | unicyclic graph | 05C69 | cactus graph | MATHEMATICS

fair domination | unicyclic graph | 05C69 | cactus graph | MATHEMATICS

Journal Article

Journal of applied mathematics & computing, ISSN 1865-2085, 2018, Volume 59, Issue 1-2, pp. 37 - 46

The first degree-based entropy of a connected graph G is defined as: $$I_1(G)=\log (\sum _{v_i\in V(G)}\deg (v_i))-\sum _{v_j\in V(G)}\frac{\deg (v_j)\log \deg...

Computational Mathematics and Numerical Analysis | Unicyclic graph | Bicyclic graph | Mathematics of Computing | Mathematical and Computational Engineering | Tree | Mathematics | Theory of Computation | Entropy | Degree sequence | MATHEMATICS | MATHEMATICS, APPLIED | Graphs | Graph theory | Mathematical analysis

Computational Mathematics and Numerical Analysis | Unicyclic graph | Bicyclic graph | Mathematics of Computing | Mathematical and Computational Engineering | Tree | Mathematics | Theory of Computation | Entropy | Degree sequence | MATHEMATICS | MATHEMATICS, APPLIED | Graphs | Graph theory | Mathematical analysis

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 11/2015, Volume 30, Issue 4, pp. 1125 - 1137

Let $$G$$ G be a connected graph with vertex set $$V(G)$$ V ( G ) . The multiplicatively weighted Harary index of a graph $$G$$ G is defined as $$H_M(G)=\sum...

Unicyclic graph | 05C50 | Degree | Mathematics | Theory of Computation | Optimization | Multiplicatively weighted Harary index | Harary index | Convex and Discrete Geometry | Operations Research/Decision Theory | 05C07 | Tree | Mathematical Modeling and Industrial Mathematics | Combinatorics | Distance | 05C15 | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BICYCLIC GRAPHS

Unicyclic graph | 05C50 | Degree | Mathematics | Theory of Computation | Optimization | Multiplicatively weighted Harary index | Harary index | Convex and Discrete Geometry | Operations Research/Decision Theory | 05C07 | Tree | Mathematical Modeling and Industrial Mathematics | Combinatorics | Distance | 05C15 | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BICYCLIC GRAPHS

Journal Article

Discrete Mathematics, Algorithms and Applications, ISSN 1793-8309, 10/2018, Volume 10, Issue 5

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 04/2014, Volume 446, pp. 115 - 132

Let G be a simple graph with n vertices and e(G) edges, and q1(G)⩾q2(G)⩾⋯⩾qn(G)⩾0 be the signless Laplacian eigenvalues of G. Let Sk+(G)=∑i=1kqi(G), where k=1,2,…,n. F. Ashraf et al...

Connected graph | Unicyclic graph | Bicyclic graph | Tricyclic graph | Signless Laplacian eigenvalues | Conjecture | GRAPH | MATHEMATICS | MATHEMATICS, APPLIED | SUM

Connected graph | Unicyclic graph | Bicyclic graph | Tricyclic graph | Signless Laplacian eigenvalues | Conjecture | GRAPH | MATHEMATICS | MATHEMATICS, APPLIED | SUM

Journal Article

Match, ISSN 0340-6253, 2014, Volume 72, Issue 3, pp. 761 - 774

The general sum-connectivity index of a graph G is a molecular descriptor defined as chi(alpha)(G) = Sigma...

COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | TREES | (N,N+1)-GRAPHS | UNICYCLIC GRAPHS | CHEMISTRY, MULTIDISCIPLINARY

COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | TREES | (N,N+1)-GRAPHS | UNICYCLIC GRAPHS | CHEMISTRY, MULTIDISCIPLINARY

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 02/2017, Volume 218, pp. 98 - 112

For a connected graph G=(V(G),E(G)) and two disjoint subsets of V(G) A={α1,…,αk} and B={β1,…,βk}, a paired (many-to-many) k-disjoint path cover of G joining A and B is a vertex-disjoint path cover...

Cube of graph | Unicyclic graph | Disjoint path cover | Spanning tree | Hamiltonian path | Linear-time algorithm | SHORT PROOF | MATHEMATICS, APPLIED | SQUARE ROOTS | FLEISCHNERS THEOREM | POWERS | HYPERCUBES | RECURSIVE CIRCULANTS G(2(M) | FAULTY ELEMENTS | PARTITIONS | EDGES | Algorithms | Computer science

Cube of graph | Unicyclic graph | Disjoint path cover | Spanning tree | Hamiltonian path | Linear-time algorithm | SHORT PROOF | MATHEMATICS, APPLIED | SQUARE ROOTS | FLEISCHNERS THEOREM | POWERS | HYPERCUBES | RECURSIVE CIRCULANTS G(2(M) | FAULTY ELEMENTS | PARTITIONS | EDGES | Algorithms | Computer science

Journal Article

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