Inverse whole domination in graphs

Omran, Ahmed A.; Ibrahim, Thaer A.

doi:10.1063/5.0067086

Cited by 1 publication

(1 citation statement)

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“…The odd geo-domination number of a graph is introduced by Anto Kinsley A and Karthika K John in the year 2020 6 . Motivated by the notion of the above parameters and their applicability, the odd (even) sum degree edge dominating set (oded (eded) -set) is introduced by posting odd (even) condition on the sum of degree of edges of edge dominating set of a graph G. In this paper, by extending the above concept on coedge dominating set, the co-odd (even) sum degree edge dominating set is defined for a graph G [7][8][9] . Then the corresponding co-odd (even) sum degree edge domination number and value are defined and studied.…”

Section: Introductionmentioning

confidence: 99%

A Study on Co – odd (even) Sum Degree Edge Domination Number in Graphs

Usha¹,

Ilakkiya²

2023

Baghdad Sci.J

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An edge dominating set of a graph is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G. The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domination value is defined. Further, the exact values of the above said parameters are found for some standard classes of graphs. The bounds of the co-odd (even) sum degree edge domination number are obtained in terms of basic graph terminologies. The co-odd (even) sum degree edge dominating sets are characterized. The relationships with other edge domination parameters are also studied.

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Section: Introductionmentioning

confidence: 99%