THE P3-DOMINATION IN GRAPHS
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Let G be a graph and u,v be any vertices of G. Then u and v are said to be P3-adjacent vertices of G if there is a subgraph of G, isomorphic to P3, Containing u and v. A P3-dominating set of G is a set D of vertices such that every vertex of G belongs to D or is P3-adjacent to a vertex of D. The P3-domination number of G denoted by P3 (G) is the minimum cardinality among the P3-dominating sets of vertices of G. In this paper we introduce and study the P3-domination of a graph G and analogous to this concept we define the P3-independence number P3 (G), P3-neighbourhood number P3 (G) and P3-domatic number dP3 (G). Some bounds and interesting results are obtained. Also the P3-adjacency motivated us to define new graphs in particular P3-neighbourhood graph, P3-complete graph, P3-regular graph, P3-complement graph and P3-complementary graph, some basic properties of these graphs are introduce and new method to construct any r-regular graph is established. finally we generalize the domination of graphs.
Abstract
Let G be a graph and u,v be any vertices of G. Then u and v are said to be P3-adjacent vertices of G if there is a subgraph of G, isomorphic to P3, Containing u and v. A P3-dominating set of G is a set D of vertices such that every vertex of G belongs to D or is P3-adjacent to a vertex of D. The P3-domination number of G denoted by P3 (G) is the minimum cardinality among the P3-dominating sets of vertices of G. In this paper we introduce and study the P3-domination of a graph G and analogous to this concept we define the P3-independence number P3 (G), P3-neighbourhood number P3 (G) and P3-domatic number dP3 (G). Some bounds and interesting results are obtained. Also the P3-adjacency motivated us to define new graphs in particular P3-neighbourhood graph, P3-complete graph, P3-regular graph, P3-complement graph and P3-complementary graph, some basic properties of these graphs are introduce and new method to construct any r-regular graph is established. finally we generalize the domination of graphs.
참고문헌 (9)
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