Neighborhood contraction in graphs

S. S. Kamath () and Prameela Kolake ()
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S. S. Kamath: National Institute of Technology Karnataka
Prameela Kolake: National Institute of Technology Karnataka

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 1, 97-110

Abstract: Abstract Let G be a graph and v be any vertex of G. Then the neighborhood contracted graph G v of G, with respect to the vertex v, is the graph with vertex set V − N(v), where two vertices u,w ∈ V − N(v) are adjacent in G v if either w = v and u is adjacent to any vertex of N(v) in G or u,w ∉ N[v] and u,w are adjacent in G. The properties of the neighborhood contracted graphs are discussed in this paper. The neighborhood contraction in some special class of graphs, the domination in a graph and the neighborhood contracted graphs are discussed in the paper.

Keywords: Neighborhood; degree; induced subgraph; contraction; domination (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-015-0169-9

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