Maximizing the Zagreb indices of (n,m)-graphs

Kexiang Xu; Kinkar Ch Das; S. Balachandran

Maximizing the Zagreb indices of (n,m)-graphs

Kexiang Xu, Kinkar Ch Das, S. Balachandran

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

92 Scopus citations

Abstract

For a (molecular) graph, the first and second Zagreb indices (M₁ and M₂) are two well-known topological indices in chemical graph theory introduced in 1972 by Gutman and Trinajstić. Let Gn,m be the set of connected graphs of order n and with m edges. In this paper we characterize the extremal graphs from G_n,m with n + 2 ≥ m ≥ 2n-4 with maximal first Zagreb index and from G_n,m with m-n = (^k₂)-k for k ≥ 4 with maximal second Zagreb index, respectively. Finally a related conjecture has been proposed to the extremal graphs with respect to second Zagreb index.

Original language	English
Pages (from-to)	641-654
Number of pages	14
Journal	Match
Volume	72
Issue number	3
State	Published - 2014

Cite this

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abstract = "For a (molecular) graph, the first and second Zagreb indices (M1 and M2) are two well-known topological indices in chemical graph theory introduced in 1972 by Gutman and Trinajsti{\'c}. Let Gn,m be the set of connected graphs of order n and with m edges. In this paper we characterize the extremal graphs from Gn,m with n + 2 ≥ m ≥ 2n-4 with maximal first Zagreb index and from Gn,m with m-n = (k2)-k for k ≥ 4 with maximal second Zagreb index, respectively. Finally a related conjecture has been proposed to the extremal graphs with respect to second Zagreb index.",

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AB - For a (molecular) graph, the first and second Zagreb indices (M1 and M2) are two well-known topological indices in chemical graph theory introduced in 1972 by Gutman and Trinajstić. Let Gn,m be the set of connected graphs of order n and with m edges. In this paper we characterize the extremal graphs from Gn,m with n + 2 ≥ m ≥ 2n-4 with maximal first Zagreb index and from Gn,m with m-n = (k2)-k for k ≥ 4 with maximal second Zagreb index, respectively. Finally a related conjecture has been proposed to the extremal graphs with respect to second Zagreb index.

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JO - Match

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Maximizing the Zagreb indices of (n,m)-graphs

Abstract

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