On Entire Dominating Transformation Graphs and Fuzzy Transformation Graphs

V Kulli
2015 Intern. J. Fuzzy Mathematical Archive   unpublished
Let G=(V, E) be a graph. Let S be the set of all minimal dominating sets of G. Let x, y, z be three variables each taking value + or-. The entire transformation graph G xyz is the graph having V∪S as the vertex set and for any two vertices u and v in V ∪ S, u and v are adjacent in G xyz if and only if one of the following conditions holds: (i) u, v ∈ V. x = + if u, v ∈D where D is a minimal dominating set of G. x =-if u, v ∉ D where D is a minimal dominating set of G. (ii) u, v ∈ S. y = + if u
more » ... v ≠ φ. y=-if u ∩ v = φ (iii) u ∈ V and v ∈ S. z = + if u ∈ v. z =-if u ∉ v. In this paper, we initiate a study of entire dominating transformation graphs in domination theory. Also we introduce some fuzzy transformation graphs.