Sep 2026· Asian-European Journal of Mathematics· 0 citations
Abstract
A semitotal dominating set of a nontrivial connected graph G is a dominating set D of G such that every vertex in D is within distance two of another vertex in D. The semitotal domination number of G is the minimum cardinality among all semitotal dominating sets of G. In this article, we investigate the semitotal domination number of rooted product graphs. We derive exact formulas for this parameter and show that it can be expressed in terms of several domination parameters of the factor graphs. Furthermore, we characterize the graph families for which each of the obtained expressions is attained.
Fundamental properties of the resilient domination number are established and corresponding bounds and explicit formulas for the resilient domination number are obtained.
Carren C. Sibongga, Mae P. Militante, D. J. Tejada et al.· Far East Journal of Mathemat...· 0 citations
Let G be a nontrivial graph. A set D ⊆ V(G) is a double dominating set of G if |
\mathrm{N_G}
[v] ∩ D| ≥ 2 for every vertex v ∈ V(G), where
\mathrm{N_G}
[v] represents the closed neighborhood of v. The double domination number of G is the minimum cardinality among all double dominating sets of G. In this paper we...
A. Cabrera-Martínez, Ismael Rios-Villamar, J. Sigarreta· Filomat· 1 citation
For a subgraph of a vertex set of a graph to be strong efficient, all remaining vertices in the graph must have exactly one neighbor of equal or greater degree in the specified subgraph and all vertices in the specified subgraph are independent of each other. The strong efficient domination number is the cardinality of...
Betul Atay· Communications faculty of sc...· 0 citations
A dominating set $D$ of a nontrivial connected graph $G$ is called a semitotal dominating set of $G$ if every vertex in $D$ is at distance at most two from another vertex in $D$. If, in addition, $D$ is an independent set, then $D$ is called an independent semitotal dominating set of $G$. The (independent) semitotal do...
A. Cabrera-Martínez, J. L. López-Carmona, Ismael Rios-Villamar et al.· 0 citations
In this paper, we establish the study of outer-connected semitotal double Roman domination. A function f is said to be an outer-connected semitotal double Roman dominating function of a graph G if it is a double dominating function and satisfies the condition for outer-connected semitotal. Our results consist of some b...
A. Aradais· International Journal of Mat...· 0 citations
Let G be a non-trivial graph. A dominating set I ⊂ V (G) is called an Isolate Pendant Dominating set (IPD-set) if the induced subgraph 〈I〉 has maximum degree at most one and contains at least one isolate vertex and at least one pendant vertex. The minimum cardinality of an IPD-set is called the IP domination number a...
AL. Yakavi, A. Mydeen Bibi· Reserche operationelle· 0 citations
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