Theoretical analysis uncovers accurate degree domination bounds in standard graph families, highlighting structural constraints on degree dominating sets.
Consider a graph πΊ(π, πΈ) and a dominating set π·π, the degree of a dominating set π·π is the sum of the degree of all the vertices in π·π and is written as πππ(π·π). The degree of the set is the sum of the degrees of all the vertices of the set. The minimum degree among all the dominating sets is called the degree dominating set and is written as π·π . Now, a dominating set π·π is an accurate degree dominating set if π β π·π has no degree dominating set of the cardinality of π·π . The accurate degree domination number πΎπ Β° (πΊ) of a given graph πΊ is the minimum number of vertices in an accurate degree dominating set of πΊ. This paper initiates the study of an accurate degree domination number π€π Β° (πΊ). Further, obtain some bounds for πΎπ Β° (πΊ), and the numerical value of πΎπ Β° (πΊ) some standard graphs like path, cycle, wheel, complete graph, complete bipartite graph.
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Chatterjee et al. (2024) studied this question.
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