No abstract

In this article, we consider the bipartite graphs K 2 × K n . We first show that the connectedness of N (K Kn n+1 ) = 0. Further, we show that Hom(K 2 × K n , K m ) is homotopic to S m−2 , if 2 ≤ m < n.

No abstract

The clique complex of a graph G is a simplicial complex whose simplices are all the cliques of G, and the line graph L(G) of G is a graph whose vertices are the edges of G and the edges of L(G) are incident edges of G. In this article, we determine the homotopy type of the clique complexes of line graphs for several classes of graphs including trianglefree graphs, chordal graphs, complete multipartite graphs, wheel-free graphs, and 4-regular circulant graphs. We also give a closed form formula for the homotopy type of these complexes in several cases.

In this note we characterize strongly regular graphs which are stable.