Domination versus edge domination

Julien Baste; Maximilian Fürst; Michael A. Henning; Elena Mohr; Dieter Rautenbach

doi:10.1016/j.dam.2020.05.030

Domination versus edge domination

Julien Baste
, Maximilian Fürst
, Michael A. Henning
, Elena Mohr
, Dieter Rautenbach

Mathematics and Applied Mathematics

Ulm University

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

5 Citations (Scopus)

Abstract

We propose the conjecture that the domination number γ(G) of a Δ-regular graph G with Δ≥1 is always at most its edge domination number γ_e(G), which coincides with the domination number of its line graph. We prove that γ(G)≤1+[Formula presented]γ_e(G) for general Δ≥1, and γ(G)≤[Formula presented]γ_e(G) for Δ=3. Furthermore, we verify our conjecture for cubic claw-free graphs.

Original language	English
Pages (from-to)	343-349
Number of pages	7
Journal	Discrete Applied Mathematics
Volume	285
DOIs	https://doi.org/10.1016/j.dam.2020.05.030
Publication status	Published - 15 Oct 2020

Keywords

Domination
Edge domination
Minimum maximal matching

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2020.05.030

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title = "Domination versus edge domination",

abstract = "We propose the conjecture that the domination number γ(G) of a Δ-regular graph G with Δ≥1 is always at most its edge domination number γe(G), which coincides with the domination number of its line graph. We prove that γ(G)≤1+[Formula presented]γe(G) for general Δ≥1, and γ(G)≤[Formula presented]γe(G) for Δ=3. Furthermore, we verify our conjecture for cubic claw-free graphs.",

keywords = "Domination, Edge domination, Minimum maximal matching",

author = "Julien Baste and Maximilian F{\"u}rst and Henning, \{Michael A.\} and Elena Mohr and Dieter Rautenbach",

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year = "2020",

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doi = "10.1016/j.dam.2020.05.030",

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T1 - Domination versus edge domination

AU - Baste, Julien

AU - Fürst, Maximilian

AU - Henning, Michael A.

AU - Mohr, Elena

AU - Rautenbach, Dieter

PY - 2020/10/15

Y1 - 2020/10/15

N2 - We propose the conjecture that the domination number γ(G) of a Δ-regular graph G with Δ≥1 is always at most its edge domination number γe(G), which coincides with the domination number of its line graph. We prove that γ(G)≤1+[Formula presented]γe(G) for general Δ≥1, and γ(G)≤[Formula presented]γe(G) for Δ=3. Furthermore, we verify our conjecture for cubic claw-free graphs.

AB - We propose the conjecture that the domination number γ(G) of a Δ-regular graph G with Δ≥1 is always at most its edge domination number γe(G), which coincides with the domination number of its line graph. We prove that γ(G)≤1+[Formula presented]γe(G) for general Δ≥1, and γ(G)≤[Formula presented]γe(G) for Δ=3. Furthermore, we verify our conjecture for cubic claw-free graphs.

KW - Domination

KW - Edge domination

KW - Minimum maximal matching

UR - https://www.scopus.com/pages/publications/85086599676

U2 - 10.1016/j.dam.2020.05.030

DO - 10.1016/j.dam.2020.05.030

M3 - Article

AN - SCOPUS:85086599676

SN - 0166-218X

VL - 285

SP - 343

EP - 349

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Domination versus edge domination

Abstract

Keywords

ASJC Scopus subject areas

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