ON THE TRANSFORMATION GRAPH G+--

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Published: 2016-10-27

Page: 83-89


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


How to Cite

TELI, V. V., & PATIL, P. V. (2016). ON THE TRANSFORMATION GRAPH G+--. Asian Journal of Mathematics and Computer Research, 14(2), 83–89. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/675

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