On linear combinations between Zagreb indices/coindices of a line graph

Document Type : Special Issue of JDMA in the Memory of Prof. Ali Reza Ashrafi

Authors

Faculty of Electronic Engineering, University of Nis, Nis, Serbia

Abstract

Let $G=(V,E)$, $V=\left\{ v_{1},v_{2},\ldots ,v_{n}\right\}$, be a simple graph of order $n$ and size $m$.
Denote by $\Delta = d_1\ge d_2 \ge \cdots \ge d_n= \delta$, $d_i=d(v_i)$, and $\Delta_e=d(e_1)\ge d(e_2)\ge \cdots \ge d(e_m)=\delta_e$, sequences of vertex and edge degrees, respectively. The first reformulated Zagreb index (coindex) is defined as $\displaystyle EM_1(G)=\sum_{i=1}^m d(e_i)^2 = \sum_{e_i\sim e_j}(d(e_i)+d(e_j))$ $\Big(\displaystyle \overline{EM}_1(G) = \sum_{e_i\nsim e_j}(d(e_i)+d(e_j))\Big)$.
We consider relationship between reformulated Zagreb indices/coindices and determine their bounds in terms of some basic graph parameters.

Graphical Abstract

On linear combinations between Zagreb indices/coindices of a line graph

Keywords

Main Subjects


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Volume 8, Issue 2
July 2023
Pages 65-74
  • Receive Date: 27 May 2023
  • Revise Date: 03 June 2023
  • Accept Date: 15 June 2023
  • Publish Date: 01 July 2023