Induced cycles vertex number and (1,2)-domination in cubic graphs

Rija Erveš and Aleksandra Tepeh

Applied Mathematics and Computation, 2026, vol. 510, issue C

Abstract: A (1,2)-dominating set in a graph G is a set S such that every vertex outside S has at least one neighbor in S, and each vertex in S has at least two neighbors in S. The (1,2)-domination number, γ1,2(G), is the minimum size of such a set, while cind(G) is the cardinality of the largest vertex set in G that induces one or more cycles. In this paper, we initiate the study of a relationship between these two concepts and discuss how establishing such a connection can contribute to solving a conjecture on the lower bound of cind(G) for cubic graphs. We also establish an upper bound on cind(G) for cubic graphs and characterize graphs that achieve this bound.

Keywords: Cubic graphs; (1,2)-Domination; Induced 2-regular subgraphs; Induced cycles vertex number (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:510:y:2026:i:c:s0096300325004266

DOI: 10.1016/j.amc.2025.129700

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