Sep 2026· Reserche operationelle· Vol 60, pp. 2955-2967· 0 citations
Abstract
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 and is denoted by γ01(G). In this paper, we study the IP domination numberbfor semi-total point graphs. We determine exact values of γ_{01}(T_2(G)) for several well-known graph classes, including paths, cycles, and complete graphs. Furthermore, we provide a characterization of IPD-sets in the join of two graphs and examine the behavior of γ01 under the join operation for both arbitrary graphs and semi-total point graphs. Finally, we obtain lower and upper bounds for γ_{01}(T_2(G)) in terms of the order and size of G. The practical relevance of the proposed concepts is illustrated through an application in pest control management.
An isolated signed dominating function (ISDF) on a graph $G$ is a signed dominating function whose closed neighborhood sum is equal to $1$ for at least one vertex. The minimum weight of such a function is called the isolated signed domination number, denoted by $\gamma_{is}(G)$. This notion was introduced by Dayana and...
H. Rahbani, Hossein Abdollahzadeh Ahangar, M. Kheibari et al.· Reserche operationelle· 0 citations
This paper develops an exact algorithm based on the Branch and Bound approach for solving PIDS on chordal graphs, which involves identifying the smallest group of vertices in a given network that maximizes influence throughout the network.
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A resilient dominating set in a graph is a dominating set in which each vertex has at least one neighbor within the set and at least one neighbor outside the set, and the weakly induced subgraph of the set is connected. The smallest cardinality of such a set is the resilient domination number. This paper establishes fu...
Carren C. Sibongga, Mae P. Militante, D. J. Tejada et al.· Far East Journal of Mathemat...· 0 citations
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 domin...
A. Cabrera-Martínez, J. L. López-Carmona, José M. Rodríguez et al.· Asian-European Journal of Ma...· 0 citations
Baste et al. (2020) conjectured that every regular graph of positive degree has domination number at most its edge domination number, the least size of a maximal matching. Combining published bounds settles the inequality for every degree at least nine. A reduction proves the inequality whenever one endpoint of each ed...
This work establishes general properties of k -total bondage and finds exact values for certain graph classes including paths, cycles, wheels, complete and complete bipartite graphs.
Unknown authors· 0 citations
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