A Note on the Signed Clique Domination Numbers of Graphs. (17th September 2022)

• Record Type: Journal Article
• Authors: Xu, Baogen; Lan, Ting; Zheng, Mengmeng
• Other Names: Araci Serkan Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2022(2022)
• Publication Date: 2022-09-17
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2022/3208164
• Languages: English
• ISSNs: 2314-4629

Abstract

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 .