Abstract. Recently, M. Abért and T. Hubai studied the following problem. The chromatic measure of a finite simple graph is defined to be the uniform distribution on its chromatic roots. Abért and… (More)

We will prove that the path minimizes the number of closed walks of length l among the connected graphs for all l. Indeed, we will prove that the number of closed walks of length l and many other… (More)

We introduce the matching measure of a finite graph as the uniform distribution on the roots of the matching polynomial of the graph. We analyze the asymptotic behavior of the matching measure for… (More)

Friedland’s Lower Matching Conjecture asserts that if G is a d–regular bipartite graph on v(G) = 2n vertices, and mk(G) denotes the number of matchings of size k, then mk(G) ≥ ( n k )2( d− p d… (More)

Let H be a graph on n vertices and let the blow-up graph G[H] be defined as follows. We replace each vertex vi of H by a cluster Ai and connect some pairs of vertices of Ai and Aj if (vi, vj) was an… (More)

In this paper we study several problems concerning the number of homomorphisms of trees. We begin with an algorithm for the number of homomorphisms from a tree to any graph. By using this algorithm… (More)

In this paper we study various extremal problems related to some combinatorially defined graph polynomials such as matching polynomial, chromatic polynomial, Laplacian polynomial. It will turn out… (More)

In this paper we construct trees having only integer eigenvalues with arbitrarily large diameters. In fact, we prove that for every set S of positive integers there exists a tree whose positive… (More)

One can define the adjoint polynomial of the graph G as follows. Let ak(G) denote the number of ways one can cover all vertices of the graph G by exactly k disjoint cliques of G. Then the adjoint… (More)