The restrained double Roman domination and graph operations

Zhipeng Gao, Changqing Xi and Jun Yue

Applied Mathematics and Computation, 2025, vol. 495, issue C

Abstract: A restrained double Roman dominating function (RDRD-function) on a graph G is a function f:V(G)→{0,1,2,3} that satisfies two conditions: (1) If f(v)<2, then ∑u∈NG[v]f(u)≥|ANGf(v)|+2, where ANGf(v)={u∈NG(v):f(u)≥1}; (2) The subgraph induced by the vertices assigned 0 under f contains no isolated vertices. The weight of an RDRD-function f is ∑v∈V(G)f(v), and the minimum weight of an RDRD-function on G is defined as the restrained double Roman domination number (RDRD-number) of G, denoted by γrdR(G). In this paper, we first establish that computing the RDRD-number is NP-hard, even for chordal graphs. Then the impact of various graph operations, including the strong product, cardinal product, and corona product, on the restrained double Roman domination number are given.

Keywords: Double Roman domination; Restrained double Roman domination number; NP-hard; Graph operations (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000426

DOI: 10.1016/j.amc.2025.129315

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