Pendant domination in double graphs
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Let G be any graph. A subset S of vertices in G is called a dominating set if every vertex in V -S is adjacent to atleast one vertex in S. A dominating set S is called a pendant dominating set if the induced subgraph of S contains at least one pendant vertex. The minimum cardinality of a pendant dominating set is called the pendant domination number denoted by pe. In this paper, we are considering special types of graphs called double graphs obtained through a graph operation. We study the pendant domination for these graphs. We calculate the exact value of pendant domination number in double graphs of some standard class of graphs. Further, the bounds are estimated for these parameter in terms of order and degree of a graph.
Abstract
Let G be any graph. A subset S of vertices in G is called a dominating set if every vertex in V -S is adjacent to atleast one vertex in S. A dominating set S is called a pendant dominating set if the induced subgraph of S contains at least one pendant vertex. The minimum cardinality of a pendant dominating set is called the pendant domination number denoted by pe. In this paper, we are considering special types of graphs called double graphs obtained through a graph operation. We study the pendant domination for these graphs. We calculate the exact value of pendant domination number in double graphs of some standard class of graphs. Further, the bounds are estimated for these parameter in terms of order and degree of a graph.
참고문헌 (4)
- Mojdeh, D.A, "Doimnation in Jahangir graph J2;m", Int. J.Contemp. Math. Sciences, 2(24), pp.1193~1199 (2007)
- Munarini, E, "Double Graphs", Discrete Mathematics, 308, pp.242~254 (2008)
- Nayaka S.R, "Pendant Domination in Graphs", Journal of Combinatorial Mathematics and Combinatorial computing, 112, pp.219~230 (2020)
- Nayaka S.R, "Pendant Domination in some Gener-alised Graphs", International Journal of Scientific Engineering and Science, 1(7), pp.13~15 (2017)