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… Expand

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.Expand

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.Expand

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.Expand

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… Expand

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.Expand

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.Expand

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… Expand

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.Expand