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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
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
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
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
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
Journal Article
PLoS ONE, ISSN 1932-6203, 06/2015, Volume 10, Issue 6, p. e0129497
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
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
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 11/2014, Volume 30, Issue 6, pp. 1551 - 1563
Journal Article
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
Journal Article
Applicable analysis and discrete mathematics, ISSN 1452-8630, 10/2017, Volume 11, Issue 2, pp. 273 - 298
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
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
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 11/2015, Volume 30, Issue 4, pp. 1125 - 1137
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
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
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
Journal Article
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