The signed edge-domatic number of nearly cubic graphs

Jia-Xiong Dan, Zhi-Bo Zhu, Xin-Kui Yang, Ru-Yi Li, Wei-Jie Zhao and Xiang-Jun Li ()
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Jia-Xiong Dan: Yangtze University
Zhi-Bo Zhu: Yangtze University
Xin-Kui Yang: Yangtze University
Ru-Yi Li: Yangtze University
Wei-Jie Zhao: Yangtze University
Xiang-Jun Li: Yangtze University

Journal of Combinatorial Optimization, 2022, vol. 44, issue 1, No 21, 435-445

Abstract: Abstract A signed edge-domination of graph G is a function $$f:\ E(G)\rightarrow \{+1,-1\}$$ f : E ( G ) → { + 1 , - 1 } such that $$\sum _{e'\in N_{G}[e]}{f(e')}\ge 1$$ ∑ e ′ ∈ N G [ e ] f ( e ′ ) ≥ 1 for each $$e\in E(G)$$ e ∈ E ( G ) . A set $$\{ f_1,f_2,\ldots , f_d \}$$ { f 1 , f 2 , … , f d } of the signed edge-domination of G is called a family of signed edge-dominations of G if $$\sum _{i=1}^{d}{f_i(e)}\le 1 $$ ∑ i = 1 d f i ( e ) ≤ 1 for every $$e \in E(G)$$ e ∈ E ( G ) . The largest number of a family of signed edge-dominations of G is the signed edge-domatic number of G. This paper studies the signed edge-domatic number of nearly cubic graph, and determines this parameter for a class of graphs.

Keywords: Domination; Domatic number; Nearly cubic graph; Signed edge-domination (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00843-w

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