Cliques and Clique Covers in Interval-Valued Fuzzy Graphs

Abstract

Finding cliques and clique covers in graphs are one of the most needful tasks. In this paper, interval-valued fuzzy cliques (IVFQs) and interval-valued fuzzy clique covers (IVFQCs) of an interval-valued fuzzy graph (IVFG) are introduced by introducing the fuzziness because, the crisp graphs has some limitations in real world due to uncertainty of vagueness. Here, the concept of cliques and clique covers are slightly modified so that every IVFQ is complete. Also, a clique cover of a crisp graph always covers all the edges and vertices of the graph whereas, the IVFQCs obtained by fuzzify to the clique covers does not satisfy the property. Hence, the definition is modified and studied some theorems on it. To better understand the useability of this work a model application is stated in this paper.