Contents

Ars Combinatoria

  • Research article

On First Zagreb index, \({\tau}\)-path-coverable and \({\tau}\)-edge-Hamiltonian graphs

Mingqiang An1, Runli Tian2, Huiya Yan3
1College of Science, Tianjin University of Science and Technology, Tianjin, 300457, P.R. China
2School of Software Engineering, Changsha Institute of Technology, Changsha, 410200, P.R. China
3Mathematics and Statistics Department, University of Wisconsin-La Crosse, La Crosse, WI 54601, USA
  • Received: 17/08/2024
  • Accepted: 11/03/2025
  • Published Online: 22/03/2025

Abstract

Given a connected graph \(H\), its first Zagreb index \(M_{1}(H)\) is equal to the sum of squares of the degrees of all vertices in \(H\). In this paper, we give a best possible lower bound on \(M_{1}(H)\) that guarantees \(H\) is \(\tau\)-path-coverable and \(\tau\)-edge-Hamiltonian, respectively. Our research supplies a continuation of the results presented by Feng et al. (2017).

Keywords: Zagreb index, \(\tau\)-path-coverable, \(\tau\)-edge-Hamiltonian
Information
Guidelines
CP Initiatives
Follow CP
Facebook X-twitter Linkedin

1970-2025 CP (Manitoba, Canada) unless otherwise stated.

Citation
Mingqiang An, Runli Tian, Huiya Yan. On First Zagreb index, \({\tau}\)-path-coverable and \({\tau}\)-edge-Hamiltonian graphs[J], Ars Combinatoria, Volume 162. 31-38. https://www.doi.org/10.61091/ars162-03.