A Note on the Signed Clique Domination Numbers of Graphs

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∈EKfe≥1 holds for every nontrivial clique K in G. The signed clique domination number of G is defined as γscl′G=min∑e∈EGfe|fis an SCDF ofG. In this paper, we investigate the signed clique do...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2022, Vol.2022 (1)
Main Authors: Xu, Baogen, Lan, Ting, Zheng, Mengmeng
Format: Article
Language:English
Subjects:
Graphs
Inequality
Labeling
Mathematical functions
Mathematics
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Summary: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∈EKfe≥1 holds for every nontrivial clique K in G. The signed clique domination number of G is defined as γscl′G=min∑e∈EGfe|fis an SCDF ofG. 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 Pm∨Kn¯ and Cm∨Kn.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/3208164