Edge domination in some brick product graphs
Citation
Kumar, U. V. C., Murali, R. & Girisha, A. (2020). Edge domination in some brick product graphs. TWMS Journal of Applied and Engineering Mathematics, 10(1), 173-180.Abstract
Let G = (V, E) be a simple connected and undirected graph. A set F of edges in G is called an edge dominating set if every edge e in E − F is adjacent to at least one edge in F. The edge domination number γ′ (G) of G is the minimum cardinality of an edge dominating set of G. The shadow graph of G, denoted D₂(G) is the graph constructed from G by taking two copies of G, say G itself and G′ and joining each vertex u in G to the neighbors of the corresponding vertex u′ in G′. Let D be the set of all distinct pairs of vertices in G and let Ds (called the distance set) be a subset of D. The distance graph of G, denoted by D(G, Ds) is the graph having the same vertex set as that of G and two vertices u and v are adjacent in D(G, Ds) whenever d(u, v) ∈ Ds. In this paper, we determine the edge domination number of the shadow distance graph of the brick product graph C(2n, m, r).
Source
TWMS Journal of Applied and Engineering MathematicsVolume
10Issue
1URI
https://hdl.handle.net/11729/2803http://jaem.isikun.edu.tr/web/index.php/archive/104-vol10no1/502
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