Equitable cototal and inverse equitable cototal domination number of the jump graph of a graph
S. E. Annie Jasmine, K. Ameenal Bibi · AIP conference proceedings · 2019
A cototal dominating set D ⊆ V [J (G)] is an equitable cototal dominating set if for every v ∈ V [J (G)] − D there is a u ∈ D with |deg(u) – deg(v)| ≤ 1. The equitable cototal domination number γect[J(G)] is the minimum cardinality among all the minimal equitable cototal dominating set of J(G). If 〈V [J (G)] − D〉 ≠ ø contains a dominating set D′ such that 〈V [J (G)] − D′〉 has no isolated vertex and |deg (c) −deg(d)| ≤ 1, then D′ is termed as the inverse equitable cototal dominating set of J (G) with respect to D. The inverse e quitable cototal domination number γect−1[J(G)] is the minimum number of vertices contained in any minimal inverse equitable cototal dominating set. This paper contains results, bounds and exact values of these parameters.