Generalized Power Domination in Claw-Free Regular Graphs

Hangdi Chen; Changhong Lu; Qingjie Ye

doi:10.1007/s00373-022-02476-0

Generalized Power Domination in Claw-Free Regular Graphs

Hangdi Chen
, Changhong Lu^*
, Qingjie Ye

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

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

Abstract

In this paper, we give a series of counterexamples to negate a conjecture and answer an open question on the k-power domination of regular graphs [see Dorbec et al. (SIAM J Discrete Math 27:1559–1574, 2013)]. Furthermore, we focus on the study of k-power domination of claw-free graphs. We show that for l∈ { 2 , 3 } and k≥ l, the k-power domination number of a connected claw-free (k+ l+ 1) -regular graph on n vertices is at most nk+l+2, and this bound is tight.

Original language	English
Article number	68
Journal	Graphs and Combinatorics
Volume	38
Issue number	3
DOIs	https://doi.org/10.1007/s00373-022-02476-0
State	Published - Jun 2022

Keywords

Claw-free graphs
Domination
Electrical systems monitoring
Power domination
Regular graphs

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10.1007/s00373-022-02476-0

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title = "Generalized Power Domination in Claw-Free Regular Graphs",

abstract = "In this paper, we give a series of counterexamples to negate a conjecture and answer an open question on the k-power domination of regular graphs [see Dorbec et al. (SIAM J Discrete Math 27:1559–1574, 2013)]. Furthermore, we focus on the study of k-power domination of claw-free graphs. We show that for l∈ \{ 2 , 3 \} and k≥ l, the k-power domination number of a connected claw-free (k+ l+ 1) -regular graph on n vertices is at most nk+l+2, and this bound is tight.",

keywords = "Claw-free graphs, Domination, Electrical systems monitoring, Power domination, Regular graphs",

author = "Hangdi Chen and Changhong Lu and Qingjie Ye",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.",

year = "2022",

month = jun,

doi = "10.1007/s00373-022-02476-0",

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T1 - Generalized Power Domination in Claw-Free Regular Graphs

AU - Chen, Hangdi

AU - Lu, Changhong

AU - Ye, Qingjie

PY - 2022/6

Y1 - 2022/6

N2 - In this paper, we give a series of counterexamples to negate a conjecture and answer an open question on the k-power domination of regular graphs [see Dorbec et al. (SIAM J Discrete Math 27:1559–1574, 2013)]. Furthermore, we focus on the study of k-power domination of claw-free graphs. We show that for l∈ { 2 , 3 } and k≥ l, the k-power domination number of a connected claw-free (k+ l+ 1) -regular graph on n vertices is at most nk+l+2, and this bound is tight.

AB - In this paper, we give a series of counterexamples to negate a conjecture and answer an open question on the k-power domination of regular graphs [see Dorbec et al. (SIAM J Discrete Math 27:1559–1574, 2013)]. Furthermore, we focus on the study of k-power domination of claw-free graphs. We show that for l∈ { 2 , 3 } and k≥ l, the k-power domination number of a connected claw-free (k+ l+ 1) -regular graph on n vertices is at most nk+l+2, and this bound is tight.

KW - Claw-free graphs

KW - Domination

KW - Electrical systems monitoring

KW - Power domination

KW - Regular graphs

UR - https://www.scopus.com/pages/publications/85126234410

U2 - 10.1007/s00373-022-02476-0

DO - 10.1007/s00373-022-02476-0

M3 - 文章

AN - SCOPUS:85126234410

SN - 0911-0119

VL - 38

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 3

M1 - 68

ER -

Generalized Power Domination in Claw-Free Regular Graphs

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