On reciprocal degree distance of graphs

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

doi:10.1016/j.heliyon.2023.e17914

On reciprocal degree distance of graphs

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

^*Corresponding author for this work

School of Computer Science

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

8 Citations (Scopus)

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Abstract

Given a connected graph H, its reciprocal degree distance is defined as R D D ( H ) = ∑ x ≠ y d H ( v x ) + d H ( v y ) d H ( v x , v y ) , where d H ( v x ) denotes the degree of the vertex v x in the graph H and d H ( v x , v y ) is the shortest distance between v x and v y 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.

Original language	English
Article number	e17914
Journal	Heliyon
Volume	9
Issue number	7
Early online date	4 Jul 2023
DOIs	https://doi.org/10.1016/j.heliyon.2023.e17914
Publication status	Published - Jul 2023

Keywords

ħ-path-coverable
ħ-hamiltonian
ħ-edge-hamiltonian
Reciprocal degree distance

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10.1016/j.heliyon.2023.e17914Licence: CC BY

1-s2.0-S2405844023051228-mainFinal published version, 354 KBLicence: CC BY

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title = "On reciprocal degree distance of graphs",

abstract = "Given a connected graph H, its reciprocal degree distance is defined as R D D ( H ) = ∑ x ≠ y d H ( v x ) + d H ( v y ) d H ( v x , v y ) , where d H ( v x ) denotes the degree of the vertex v x in the graph H and d H ( v x , v y ) is the shortest distance between v x and v y 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. ",

keywords = "ħ-path-coverable, ħ-hamiltonian, ħ-edge-hamiltonian, Reciprocal degree distance",

author = "Mingqiang An and Yinan Zhang and Das, \{Kinkar Chandra\} and Yilun Shang",

note = "Funding information: The authors would like to express their sincere gratitude to the anonymous reviewers for their valuable advice. K.C. Das is supported by National Research Foundation funded by the Korean government (Grant No. 2021R1F1A1050646).",

year = "2023",

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doi = "10.1016/j.heliyon.2023.e17914",

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T1 - On reciprocal degree distance of graphs

AU - An, Mingqiang

AU - Zhang, Yinan

AU - Das, Kinkar Chandra

AU - Shang, Yilun

N1 - Funding information: The authors would like to express their sincere gratitude to the anonymous reviewers for their valuable advice. K.C. Das is supported by National Research Foundation funded by the Korean government (Grant No. 2021R1F1A1050646).

PY - 2023/7

Y1 - 2023/7

N2 - Given a connected graph H, its reciprocal degree distance is defined as R D D ( H ) = ∑ x ≠ y d H ( v x ) + d H ( v y ) d H ( v x , v y ) , where d H ( v x ) denotes the degree of the vertex v x in the graph H and d H ( v x , v y ) is the shortest distance between v x and v y 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.

AB - Given a connected graph H, its reciprocal degree distance is defined as R D D ( H ) = ∑ x ≠ y d H ( v x ) + d H ( v y ) d H ( v x , v y ) , where d H ( v x ) denotes the degree of the vertex v x in the graph H and d H ( v x , v y ) is the shortest distance between v x and v y 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.

KW - ħ-path-coverable

KW - ħ-hamiltonian

KW - ħ-edge-hamiltonian

KW - Reciprocal degree distance

UR - https://www.scopus.com/pages/publications/85165250950

U2 - 10.1016/j.heliyon.2023.e17914

DO - 10.1016/j.heliyon.2023.e17914

M3 - Article

C2 - 37456006

SN - 2405-8440

VL - 9

JO - Heliyon

JF - Heliyon

IS - 7

M1 - e17914

ER -

On reciprocal degree distance of graphs

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Keywords

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