Forcing S-Geodetic Number of A Fuzzy Graph

Abstract

Chartrand and Zhang in 1999 introduced the idea of forcing geode- tic number of crisp graphs and determined it for several classes of graphs. In this paper, the concept is extended to fuzzy graphs using sum distance and is called the forcing s-geodetic number. A characterization of the forcing s-geodetic number depending on the s-geodetic bases present in the fuzzy graph is identified. The forcing s-geodetic number of fuzzy trees, complete fuzzy graphs and of fuzzy cycles subject to certain conditions are identified.