A Note on the Signed Clique Domination Numbers of Graphs. (17th September 2022) - Xu, Baogen; Lan, Ting; Zheng, Mengmeng
Abstract : Let G = V, E be a graph. A function f : E ⟶ − 1, + 1 is said to be a signed clique dominating function (SCDF) of G if ∑ e ∈ E K f e ≥ 1 holds for every nontrivial clique K in G . The signed clique domination number of G is defined as γ scl ′ G = min ∑ e ∈ E G f e | f is an SCDF of G . In this paper, we investigate the signed clique domination numbers of join of graphs. We correct two wrong results reported by Ao et al. (2014) and Ao et al. (2015) and determine the exact values of the signed clique domination numbers of P m ∨ K n ¯ and C m ∨ K n .