International Journal of Mathematics Trends and Technology
Volume 27 | Number 1 | Year 2015 | Article Id. IJMTT-V27P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V27P501
M. K. Angel Jebitha, "Domination Uniform Subdivision Number of Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 27, no. 1, pp. 1-5, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V27P501
Let G = (V, E) be a simple undirected graph. A subset D of V(G) is said to be dominating set if every vertex of V(G) − D is adjacent to at least one vertex in D. The minimum cardinality taken over all minimal dominating sets of G is the domination number of G and is denoted by g(G). The domination uniform subdivision number of G is the least positive integer k such that the subdivision of any k edges from G results in a graph having domination number greater than that of G and is denoted by usdg(G). In this paper, we investigate the domination uniform subdivision number of standard graphs. Also we determine the bounds of usdg and characterize the extremal graphs.
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