Topology of clique complexes of line graphs

Abstract

Clique complex of a line graph is a functor from the category of graphs to the category of simplicial complexes. Using functorial properties of this functor, we determine the homotopy type of clique complexes of line graphs for several classes of graphs. Among others, we study triangle free graphs, wheel free graphs, 4-regular circulant graphs, chordal graphs, and complete multipartite graphs. We also give a closed form formula for the homotopy type of these complexes in several cases.