Zagreb indices of graphs

doi:10.1007/s11464-015-0431-9

Front. Math. China

2015, Vol. 10

Issue (3) : 567-582 https://doi.org/10.1007/s11464-015-0431-9

RESEARCH ARTICLE

Zagreb indices of graphs

Kinkar Ch. DAS^1,^*(

),Kexiang XU²,Junki NAM¹

1. Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
2. College of Science, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China

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Abstract

The first Zagreb index M₁(G) is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index M₂(G) is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying molecular graph G. In this paper, we obtain lower and upper bounds on the first Zagreb index M₁(G) of G in terms of the number of vertices (n), number of edges (m), maximum vertex degree (Δ), and minimum vertex degree (δ). Using this result, we find lower and upper bounds on M₂(G). Also, we present lower and upper bounds on M₂(G) +M₂(G) in terms of n, m, Δ, and δ, where G denotes the complement of G. Moreover, we determine the bounds on first Zagreb coindex M₁(G) and second Zagreb coindex M₂(G). Finally, we give a relation between the first Zagreb index and the second Zagreb index of graph G.

Keywords Graph first Zagreb index second Zagreb index Narumi-Katayama index inverse degree

Corresponding Author(s): Kinkar Ch. DAS

Issue Date: 01 April 2015

Cite this article:

Kinkar Ch. DAS,Kexiang XU,Junki NAM. Zagreb indices of graphs[J]. Front. Math. China, 2015, 10(3): 567-582.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0431-9
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I3/567

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