Finding Maximal Clique In A Graph

Wiwin Apriani, Novida Sari Sihombing, Zullidar Habsyah, Saib Suwilo

Abstract: Given a simple graph G with n vertices. Furthermore, given an algorithm to get maximal clique in graph G. Clique Q of G is a set of vertices, where each vertex are connected to each other. Clique is called maximal clique when it does not have vertices that adjoinable again. For finding maximal clique Qi used the Maximal Clique Algorithm. This algorithm can be used to obtain the maximum clique on certain graph models. Maximal cliques can be very small, when a graph may contain a non-maximal clique with many vertices and a separate clique of size two which is maximal. A maximum clique is necessarily maximal clique, but does not converse. There are some types of graphs, which every maximal clique is maximum clique, that is complete graphs, triangle-free graphs, and complete multipartite graphs. But the other graphs have maximal cliques that are not maximum.

Keywords: Clique, Maximal clique, Maximum clique, and Adjoinable vertices