The polytope Q, of the convex combinations of the permutation matrices of order n is well known (Birkhoffâ€™s theorem) to be the polytope of doubly stochastic matrices of order n. In particular it isâ€¦ (More)

The exponent of a primitive digraph is the smallest integer t such that for each ordered pair of (not necessarily distinct) vertices x and y there is a path of length t from x to y. There isâ€¦ (More)

The Wiener polarity indexWP (G) of a graph G is the number of unordered pairs of vertices {u, v} of G such that the distance of u and v is equal to 3. In this paper, we obtain the relation betweenâ€¦ (More)

The RandiÄ‡ index of a graph G is defined as R(G) = âˆ‘ uâˆ¼v (d(u)d(v))âˆ’ 1 2 , where d(u) is the degree of the vertex u , and the summation goes over all pairs of adjacent vertices u, v . In this paper,â€¦ (More)

The spectral radius of connected non-regular graphs is considered. Let Î»1 be the largest eigenvalue of the adjacency matrix of a graph G on n vertices with maximum degree âˆ†. By studying theâ€¦ (More)

The nullity of a graph G, denoted by Î·(G), is the multiplicity of the eigenvalue zero in its spectrum. It is known that Î·(G) â‰¤ n âˆ’ 2 if G is a simple graph on n vertices and G is not isomorphic toâ€¦ (More)

The Wiener index of a tree T obeys the relation W (T ) = âˆ‘ e n1(e) Â· n2(e), where n1(e) and n2(e) are the number of vertices adjacent to each of the two end vertices of the edge e, respectively, andâ€¦ (More)