For given graphs G and H , let |Hom(G,H)| denote the set of graph homomorphisms from G to H . We show that for any finite, n-regular, bipartite graph G and any finite graph H (perhaps with loops), |Hom(G,H)| is maximum when G is a disjoint union of Kn,n’s. This generalizes a result of J. Kahn on the number of independent sets in a regular bipartite graph. We also give the asymptotics of the log...

A minimum spanning tree of a weighted graph is a tree of the graph which contains all the vertices of the graph and the sum of weights of all its edges are minimum among all such possible trees of the graph. In this paper, we have proposed a new technique and its corresponding algorithm to construct the minimum spanning tree of a weighted graph. This new algorithm is based on the weight matrix ...