International Journal of Research in Engineering and Applied Sciences
  • Year: 2015
  • Volume: 5
  • Issue: 8

Cototal block subdivision domination in Graphs

  • Author:
  • M.H. Muddebihal1, P. Shekanna2, Shabbier Ahmed3
  • Total Page Count: 8
  • Page Number: 177 to 184

1Professor, Department of Mathematics, Gulbarga University, Gulbarga-585106, Karnataka, India

2Research Scholar, Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India

3Professor, Department of Mathematics, Gulbarga University, Gulbarga-585106, Karnataka, India

Online published on 25 December, 2015.

Abstract

For any graph G(V, E), block subdivision graph B[S(G)] is a graph whose set of vertices is the union of the set of blocks of S(G) in which two vertices are adjacent if and only if the corresponding blocks of S(G) are adjacent. A dominating set D of a graph B[S[G]] is a cototal block dominating set, if the induced subgraph 〈V[BS[G]]-D〉 has no isolated vertices. The cototal block subdivision domination number γcbs(G) is the minimum cardinality of a cototal block subdivision dominating set of G. In this paper many bonds on γcbs(G) are obtained in terms of elements of G but not the elements of B[S[G]]. Also its relation with cubic graph and other domination parameters were established.