Please use this identifier to cite or link to this item: https://scidar.kg.ac.rs/handle/123456789/9866
Title: On the Zagreb indices equality
Authors: Abdo H.
Dimitrov D.
Gutman I.
Journal: Discrete Applied Mathematics
Issue Date: 1-Jan-2012
Abstract: For a simple graph G=(V,E) with n vertices and m edges, the first Zagreb index and the second Zagreb index are defined as M1(G)= ∑v∈Vd(v)2 and M2(G)= ∑uv∈Ed(u)d(v), where d(u) is the degree of a vertex u of G. In [28], it was shown that if a connected graph G has maximal degree 4, then G satisfies M1(G)n=M2(G)m (also known as the Zagreb indices equality) if and only if G is regular or biregular of class 1 (a biregular graph whose no two vertices of same degree are adjacent). There, it was also shown that there exist infinitely many connected graphs of maximal degree Δ=5 that are neither regular nor biregular of class 1 which satisfy the Zagreb indices equality. Here, we generalize that result by showing that there exist infinitely many connected graphs of maximal degree Δ<5 that are neither regular nor biregular graphs of class 1 which satisfy the Zagreb indices equality. We also consider when the above equality holds when the degrees of vertices of a given graph are in a prescribed interval of integers. © 2011 Elsevier B.V. All rights reserved.
URI: https://scidar.kg.ac.rs/handle/123456789/9866
Type: journal article
DOI: 10.1016/j.dam.2011.10.003
ISSN: 0166218X
SCOPUS: 82755184117
Appears in Collections:University Library, Kragujevac

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