Disjunctive domination in maximal outerplanar graphs

Michael A. Henning; Paras Vinubhai Maniya; Dinabandhu Pradhan

doi:10.1016/j.dam.2025.12.056

Disjunctive domination in maximal outerplanar graphs

Michael A. Henning
, Paras Vinubhai Maniya
, Dinabandhu Pradhan

Mathematics and Applied Mathematics

Indian Institute of Technology, Dhanbad

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

Abstract

A disjunctive dominating set of a graph G is a set D⊆V(G) such that every vertex in V(G)∖D has a neighbor in D or has at least two vertices in D at distance 2 from it. The disjunctive domination number of G, denoted by γ₂^d(G), is the minimum cardinality among all disjunctive dominating sets of G. In this paper, we show that if G is a maximal outerplanar graph of order n≥7 with k vertices of degree 2, then γ₂^d(G)≤⌊29(n+k)⌋, and this bound is sharp.

Original language	English
Pages (from-to)	24-61
Number of pages	38
Journal	Discrete Applied Mathematics
Volume	385
DOIs	https://doi.org/10.1016/j.dam.2025.12.056
Publication status	Published - 31 May 2026

Keywords

Disjunctive domination
Domination
Maximal outerplanar graphs

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2025.12.056

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title = "Disjunctive domination in maximal outerplanar graphs",

abstract = "A disjunctive dominating set of a graph G is a set D⊆V(G) such that every vertex in V(G)∖D has a neighbor in D or has at least two vertices in D at distance 2 from it. The disjunctive domination number of G, denoted by γ2d(G), is the minimum cardinality among all disjunctive dominating sets of G. In this paper, we show that if G is a maximal outerplanar graph of order n≥7 with k vertices of degree 2, then γ2d(G)≤⌊29(n+k)⌋, and this bound is sharp.",

keywords = "Disjunctive domination, Domination, Maximal outerplanar graphs",

author = "Henning, \{Michael A.\} and Maniya, \{Paras Vinubhai\} and Dinabandhu Pradhan",

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year = "2026",

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doi = "10.1016/j.dam.2025.12.056",

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T1 - Disjunctive domination in maximal outerplanar graphs

AU - Henning, Michael A.

AU - Maniya, Paras Vinubhai

AU - Pradhan, Dinabandhu

PY - 2026/5/31

Y1 - 2026/5/31

N2 - A disjunctive dominating set of a graph G is a set D⊆V(G) such that every vertex in V(G)∖D has a neighbor in D or has at least two vertices in D at distance 2 from it. The disjunctive domination number of G, denoted by γ2d(G), is the minimum cardinality among all disjunctive dominating sets of G. In this paper, we show that if G is a maximal outerplanar graph of order n≥7 with k vertices of degree 2, then γ2d(G)≤⌊29(n+k)⌋, and this bound is sharp.

AB - A disjunctive dominating set of a graph G is a set D⊆V(G) such that every vertex in V(G)∖D has a neighbor in D or has at least two vertices in D at distance 2 from it. The disjunctive domination number of G, denoted by γ2d(G), is the minimum cardinality among all disjunctive dominating sets of G. In this paper, we show that if G is a maximal outerplanar graph of order n≥7 with k vertices of degree 2, then γ2d(G)≤⌊29(n+k)⌋, and this bound is sharp.

KW - Disjunctive domination

KW - Domination

KW - Maximal outerplanar graphs

UR - https://www.scopus.com/pages/publications/105027726854

U2 - 10.1016/j.dam.2025.12.056

DO - 10.1016/j.dam.2025.12.056

M3 - Article

AN - SCOPUS:105027726854

SN - 0166-218X

VL - 385

SP - 24

EP - 61

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Disjunctive domination in maximal outerplanar graphs

Abstract

Keywords

ASJC Scopus subject areas

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