ON THE TOTAL CLOSED EDGE – NEIGHBOURHOOD GRAPH OF A GRAPH

DOI: 10.5176/2251-1911_CMCGS13.52

Authors: SANGEETA N. BHAT, B. BASAVANAGOUD

Abstract:

In this paper, we introduce the concept of the total closed edge-neighbourhood graph of a graph. We obtain some basic properties of this graph. Also we characterize those graphs whose total closed edge-neighbourhood graphs are connected. We find the girth and vertex degree of the total closed edge-neighbourhood graphs. We also present the characterizations of graphs whose total closed edge-neighbourhood graphs are planar, outerplanar and minimally non-outerplanar..

Keywords: total closed neighbourhood graphs, line splitting graphs, inner vertex number, planar graphs, total closed edgeneighbourhood graphs.