Upper and Lower Bounds for the First and Second Zagreb Indices of Quasi Bicyclic Graphs

Document Type : Research Paper

Authors

1 Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, I. R. ‎Iran

2 Department of Pure Mathematics, Ferdowsi University of Mashhad, International Campus, P. O. Box 91779−48974, Mashhad, I. R. Iran

3 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, P. O. Box 87317−53153 Kashan, I. R. Iran

10.22052/ijmc.2021.202592.1466

Abstract

The aim of this paper is to give an upper and lower bounds for the first and second Zagreb indices of quasi bicyclic graphs. For a simple graph G, we denote M1(G) and M2(G), as the sum of deg2(u) overall vertices u in G and the sum of deg(u)deg(v) of all edges uv of G, respectively. The graph G is called quasi bicyclic graph if there exists a vertex x ∈ V (G) such that G−x is a connected bicyclic graph. The results mentioned in this paper, are mostly new or an improvement of results given by authors for quasi unicyclic graphs in [1].

Keywords


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