Work

On general reduced second Zagreb index of graphs

Year: 2019

Type: article

Abstract: Recently, Furtula et al. [B. Furtula, I. Gutman, S. Ediz, On difference of Zagreb indices, Discrete Appl. Math., 2014] introduced a new vertex-degree-based graph invariant "reduced second Zagreb index" in chemical graph theory. Here we generalize the reduced second Zagreb index (call "general reduced second Zagreb index"), denoted by $GRM_{\alpha}(G)$ and is defined as: $GRM_\alpha(G)=\sum_{uv\in E(G)}(d_G(u)+\alpha)(d_G(v)+\alpha),$ where $\alpha$ is any real number and $d_G(v)$ is the degree of the vertex $v$ of $G$. Let $\mathcal{G}_n^k$ be the set of connected graphs of order $n$ with $k$ cut edges. In this paper, we study some properties of $GRM_\alpha(G)$ for connected graphs $G$. Moreover, we obtain the sharp upper bounds on $GRM_\alpha(G)$ in $\mathcal{G}_n^{k}$ for $\alpha\geq-1/2$ and characterize the extremal graphs.

Source: Hacettepe Journal of Mathematics and Statistics

DOI: 10.15672/hjms.2019.660

Authors: Batmend Horoldagva, Lkhagva Buyantogtokh, Kinkar Ch. Das, Sang-Gu Lee

Institutions: Mongolian National University of Education, National University of Mongolia, Sungkyunkwan University

Language: English

Topic: Graph theory and applications

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Research Foundation

Award: G4677838901