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All Journal Indonesian Journal of Combinatorics
P. Usha
SIT, Tumkur, VTU University
Computer Science & IT Decision Sciences, Operations Research & Management

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Computing the split domination number of grid graphs V. R. Girish; P. Usha
Indonesian Journal of Combinatorics Vol 5, No 1 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.1.1

Abstract

A set D - V is a dominating set of G if every vertex in V - D is adjacent to some vertex in D. The dominating number γ(G) of G is the minimum cardinality of a dominating set D. A dominating set D of a graph G = (V;E) is a split dominating set if the induced graph (V - D) is disconnected. The split domination number γs(G) is the minimum cardinality of a split domination set. In this paper we have introduced a new method to obtain the split domination number of grid graphs by partitioning the vertex set in terms of star graphs and also we haveobtained the exact values of γs(Gm;n); m ≤ n; m,n ≤ 24:
Co-Authors V. R. Girish