On reciprocal degree distance of graphs

Mingqiang An; Yinan Zhang; Kinkar Chandra Das; Yilun Shang

Heliyon (Jul 2023)

On reciprocal degree distance of graphs

Mingqiang An,
Yinan Zhang,
Kinkar Chandra Das,
Yilun Shang

Affiliations

Mingqiang An: College of Science, Tianjin University of Science and Technology, Tianjin, 300457, PR China
Yinan Zhang: College of Artificial Intelligence, Tianjin University of Science and Technology, Tianjin, 300457, PR China
Kinkar Chandra Das: Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea; Corresponding authors.
Yilun Shang: Department of Computer and Information Sciences, Northumbria University, Newcastle, NE1 8ST, UK; Corresponding authors.

Journal volume & issue: Vol. 9, no. 7
p. e17914

Abstract

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Given a connected graph H, its reciprocal degree distance is defined asRDD(H)=∑x≠ydH(vx)+dH(vy)dH(vx,vy), where dH(vx) denotes the degree of the vertex vx in the graph H and dH(vx,vy) is the shortest distance between vx and vy in H. The goal of this paper is to establish some sufficient conditions to judge that a graph to be ħ-hamiltonian, ħ-path-coverable or ħ-edge-hamiltonian by employing the reciprocal degree distance.

Published in Heliyon

ISSN: 2405-8440 (Online)
Publisher: Elsevier
Country of publisher: United Kingdom
LCC subjects: Science: Science (General); Social Sciences: Social sciences (General)
Website: https://www.cell.com/heliyon/home

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