Domination in Cayley graphs: A survey
Let Ω be a symmetric generating set of a finite group Γ. Assume that (Γ,Ω)be such that Γ=〈Ω〉and Ω satisfies the two conditions C1: the identity element e∉Ω and C2: if a∈Ω, then a−1∈Ω. Given (Γ,Ω)satisfying C1and C2, define a Cayley graph G=Cay(Γ,Ω)with V(G)=Γ and E(G)={(x,y)a|x,y∈Γ,a∈Ωandy=xa}. When...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2019-04-01
|
| Series: | AKCE International Journal of Graphs and Combinatorics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0972860017301160 |
| Summary: | Let Ω be a symmetric generating set of a finite group Γ. Assume that (Γ,Ω)be such that Γ=〈Ω〉and Ω satisfies the two conditions C1: the identity element e∉Ω and C2: if a∈Ω, then a−1∈Ω. Given (Γ,Ω)satisfying C1and C2, define a Cayley graph G=Cay(Γ,Ω)with V(G)=Γ and E(G)={(x,y)a|x,y∈Γ,a∈Ωandy=xa}. When Γ=Zn=〈Ω〉, it is called as circulant graph and denoted by Cir(n,Ω). In this paper, we give a survey about the results on dominating sets in Cayley graphs and circulant graphs. Keywords: Cayley graph, Unitary Cayley graph, Dominating sets, Efficient dominating sets, E-Chain |
|---|---|
| ISSN: | 0972-8600 |