Independent Lict Subdivision Domination in Graphs

M. H. Muddebihal, Naila Anjum

Abstract: Let S (G) be the subdivision graph of G. The lict graph n [S (G)] of S (G) is a graph whose vertex set is the union of the set of edges and set of cutvertices of S (G) in which two vertices are adjacent if and only if the corresponding members are adjacent or incident. A dominating set D of the lict graph n [S (G)] is an independent dominating set if D is independent in n [S (G)]. The minimum cardinality of the smallest independent dominating set of n [S (G)] is called the independent lict subdivision dominating set of G and is denoted by i_ns (G). In this paper many bounds on i_ns (G) were obtained in terms of the vertices, edges and other different parameters of G and not in terms of the elements of n [S (G)]. Further, its relation with other different dominating parameters are also obtained.

Keywords: Subdivision, Lict graph, domination number, independent domination number

How to Cite?: M. H. Muddebihal, Naila Anjum, "Independent Lict Subdivision Domination in Graphs", Volume 3 Issue 10, October 2014, International Journal of Science and Research (IJSR), Pages: 1551-1553, https://www.ijsr.net/getabstract.php?paperid=OCT14371, DOI: https://dx.doi.org/10.21275/OCT14371