The Domination Number of a Graph Pk((k1,k2),(k3,k4))

Authors

  • Monthiya Ruangnai PhD Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200
  • Sayan Panma Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200

DOI:

https://doi.org/10.26713/cma.v10i4.1248

Keywords:

Domination number, Tree, A dominating set of a graph, The domination number of a graph, The domination number of a tree

Abstract

For each k,k1,k2,k3,k4∈N, we will denote by Pk((k1,k2),(k3,k4)) a tree of k+k1+k2+k3+k4+1 vertices with the degree sequence (1,1,1,1,2,2,2,…,2,3,3). Let αk1,βk2,σk3, and δk4 be all four endpoints of the graph. Let the distance between both vertices of degree 3 be equal to k. A subset S of vertices of a graph Pk((k1,k2),(k3,k4)) is a dominating set of Pk((k1,k2),(k3,k4)) if every vertex in V(Pk((k1,k2),(k3,k4)))−S is adjacent to some vertex in S. We investigate the dominating set of minimum cardinality of a graph Pk((k1,k2),(k3,k4)) to obtain the domination number of this graph. Finally, we determine an upper bound on the domination number of a graph Pk((k1,k2),(k3,k4)).

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References

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Published

31-12-2019
CITATION

How to Cite

Ruangnai, M., & Panma, S. (2019). The Domination Number of a Graph Pk((k1,k2),(k3,k4)). Communications in Mathematics and Applications, 10(4), 745–762. https://doi.org/10.26713/cma.v10i4.1248

Issue

Vol. 10 No. 4 (2019)

Section

Research Article

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