Geodesic Iteration Number of g-contour of a Fuzzy Graph

Abstract

Purpose: In this paper, we intent to introduce the concept of gcontour nodes in fuzzy graphs and demonstrate an application of g-contour nodes in Land line telecommunication Network.Design/approach: The concept of g-contour nodes in Fuzzy graphs is explained and is supported by several examples. The geodesic iteration number of g-contour nodes in fuzzy graphs is obtained. An application of geodesic iteration number of g-contour nodes for determining the central persons in the land-line telecommunication network (LTN) is demonstrated, by means of which churning in the land-line telecommunication system can be reduced by providing a step-wise method for canvassing each and every customer in the network.Findings: It is proved that every extreme node of G is a g-contour node of G but not conversely. The g-contour of g-self-centred fuzzy graphs and of fuzzy trees is found to be a geodesic cover. The geodesic iteration number of the g-contour of a fuzzy graph is obtained. The geodesic iteration number of complete fuzzy graphs and of fuzzy trees is proved to coincide with the geodesic iteration number of their g-contours.