-A vertex v V(G) is said to be a self vertex switching of G if G is isomorphic to G v , where G v is the graph obtained from G by deleting all edges of G incident to v and adding all edges incident to v which are not in G. In [5], trees and forests are characterized, each with a self vertex switching. In [6], connected unicyclic graphs, each with a self vertex switching are characterized. In th...

Let B(2k) be the set of all bicyclic graphs on 2k(k¿ 2) vertices with perfect matchings. In this paper, we discuss some properties of the connected graphs with perfect matchings, and then determine graphs with maximal index in B(2k). c © 2004 Elsevier B.V. All rights reserved. MSC: 05c50

This paper surveys extremal properties of general sum-connectivity index χα(G) in several classes of connected graphs of given order for some values of the parameter α: a) trees; b) connected unicyclic or bicyclic graphs; c) graphs of given connectivity. Work presented as invited lecture at CAIM 2014, September 19-22, “Vasile Alecsandri” University of Bacău, Romania.

In this paper, we investigate how the Laplacian coefficients changed after some graph transformations. So, I express some results about Laplacian coefficients ordering of graphs, focusing our attention to the bicyclic graphs. Finally, as an application of these results, we discuss the ordering of graphs based on their Laplacian like energy.

Topological indices are a class of numerical invariants that predict certain physical and chemical properties molecules. Recently, two novel topological indices, named as Sombor index reduced index, were introduced by Gutman, defined where denotes the degree vertex in . In this paper, our aim is to order trees, unicyclic graphs, bicyclic graphs tricyclic with respect index. We determine first f...