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On a Relation Between
A conjecture of AutoGraphiX on the relation between the Randic index R and the algebraic connectivity a of a connected graph G is:
A Survey on the Randic Index
The general Randic index Rα(G) of a (chemical) graph G, is defined as the sum of the weights (d(u)d(v))α of all edges uv of G, where d(u) denotes the degree of a vertex u in G and α an arbitrary real…
Extremality of degree-based graph entropies
The main contribution of this paper is to prove some extremal values for the underlying graph entropy of certain families of graphs and to find the connection between the graph entropy and the sum of degree powers.
Fifty years of graph matching, network alignment and network comparison
A novel classification scheme is introduced by distinguishing between methods for deterministic and random graphs for a better understanding of the methods, their challenges and, finally, for applying the methods efficiently in an interdisciplinary setting of data science to solve a particular problem involving comparative network analysis.
Rainbow Connections of Graphs: A Survey
This survey attempts to bring together most of the results and papers that dealt with the concept of rainbow connection, including (strong) rainbow connection number, rainbow k-connectivity, k-rainbow index, rainbow vertex-connection number, algorithms and computational complexity.
Extremal Matching Energy of Bicyclic Graphs
The energy of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Recently, Gutman and Wagner proposed the concept of the matching energy (ME) and pointed out that the…
The complexity of determining the rainbow vertex-connection of a graph
- Lily Chen, Xueliang Li, Yongtang Shi
- Computer Science, MathematicsTheor. Comput. Sci.
- 17 January 2011
The complexity of determining the rainbow vertex-connection of a graph is studied and it is proved that computing rvc(G) is NP-Hard, which means that it is already NP-Complete to decide whether rVC(G)=2.
Gallai-Ramsey number for K 4
- Henry Liu, Colton Magnant, Akira Saito, I. Schiermeyer, Yongtang Shi
- Mathematics, Computer ScienceJ. Graph Theory
- 11 January 2019
This paper attacks the next case, when $H = K_5, and shows lower and upper bounds for the Gallai Ramsey number, and concludes that Fox et al.'s conjecture is false, meaning that at least one of these two conjectures must be false.
ON MOLECULAR GRAPHS WITH SMALLEST AND GREATEST ZEROTH-ORDER GENERAL RANDIĆ INDEX∗
A molecular (n,m)-graph G is a connected simple graph with n vertices, m edges and vertex degrees not exceeding 4. If d(v) denotes the degree of the vertex v , then the zeroth-order general Randić…
Interrelations of Graph Distance Measures Based on Topological Indices
This paper derives interrelations of graph distance measures by means of inequalities based on topological indices that have not been studied in this context, using the well-known Wiener index, Randić index, eigenvalue-based quantities and graph entropies.