Smriti Saxena - Department of Mathematics, Dayalbagh Educational Institute, P.O.Box ۲۸۲۰۰۵, Agra, INDIA
Antika Thapar - Department of Mathematics, Dayalbagh Educational Institute, P.O.Box ۲۸۲۰۰۵, Agra, INDIA
Richa Bansal - Department of Mathematics, Dayalbagh Educational Institute, P.O.Box ۲۸۲۰۰۵, Agra, INDIA

In this paper, a hybrid genetic algorithm (HGA) is proposed for the total fuzzy graph coloring (TFGC) problem. TFGC comprises of a graph with fuzzy vertices and edges, seeks to obtain an optimal k-coloring of that fuzzy graph such that the degree of the sum of incompatible vertices and edges is minimized. TFGC is also converted into an equivalent binary programming problem and solved using a CPLEX solver. The performance of both methods is examined on randomly generated fuzzy graphs and computational results are reported. An application based on TFGC is also explored and solved using both proposed methods.

Fuzzy graph, incompatibility degree, total chromatic number, binary programming and hybrid genetic algorithm