The node cop‐win reliability of unicyclic and bicyclic graphs

Degree distance of unicyclic and bicyclic graphs

The Inertia of Unicyclic Graphs and Bicyclic Graphs

Let G be a graph with n vertices and ν(G) be the matching number of G. The inertia of a graph G, In(G) = (n+, n−, n0) is an integer triple specifying the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G), respectively. Let η(G) = n0 denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G) = n− 2ν(G). Gu...

On the harmonic index of the unicyclic and bicyclic graphs

The harmonic index is one of the most important indices in chemical and mathematical fields. It’s a variant of the Randić index which is the most successful molecular descriptor in structure-property and structureactivity relationships studies. The harmonic index gives somewhat better correlations with physical and chemical properties comparing with the well known Randić index. The harmonic ind...

Extremal Unicyclic and Bicyclic Graphs with Respect to Harary Index

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, we determined the extremal (maximal and minimal) unicyclic and bicyclic graphs with respect to Harary index. 2010 Mathematics Subject Classification: 05C90

Unicyclic and bicyclic graphs having minimum degree distance

In this paper characterizations of connected unicyclic and bicyclic graphs in terms of the degree sequence, as well as the graphs in these classes minimal with respect to the degree distance are given. © 2007 Elsevier B.V. All rights reserved.