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

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].

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References

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Iranian Journal of Mathematical Chemistry
Volume 12, Issue 2
June 2021
Pages 79-88

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