ON THE TRANSFORMATION GRAPH G+--
VIJAY V. TELI *
Department of Mathematics, KLS's, Vishwanathrao Deshpande Rural Institute of Technology, Haliyal - 581 329, India
PRASHANT V. PATIL
Department of Mathematics, Jain College of Engineering, Belagavi - 590 014, India
*Author to whom correspondence should be addressed.
Abstract
The transformation graph G+-- of G is the graph with vertex set V(G)∪E(G) in which the vertex x and y are joined by an edge if one of the following conditions holds: (i) x,y∈V(G) and x and y are adjacent in G, (ii) x,y∈E(G) and x and y are not adjacent in G, (iii) one of x and y is in V(G) and the other is in E(G), and they are not incident in G. In this paper we obtain some basic properties of the transformation like eccentricity of G+--, girth of G+--. Finally, we establish the characterization of graph G whose transformation graph G+-- are tree and eulerian.
Keywords: Jump graph, eccentricity, girth, transformation graph