In this article all graphs are finite, simple, loopless and undirected. Given a graph G, let V (G) and E(G) be the vertex set and the edge set of G, respectively. The order of G is |V (G)| and the size of G is |E(G)|. A vertex u is a neighbor of vertex v in G if u and v are adjacent in G. The open neighborhood of v, NG(v), consists of all neighbors of v in G, and the closed neighborhood of v, NG[v], is equal to NG(v)∪{v}. A vertex v of G is called an isolated vertex of G if v has no neighbors… Expand

It is shown that the addition of a single edge between a pair of nonadjacent vertices in a graph of order $n$ can decrease the mean subtree order by as much as $n/3$ asymptotically.Expand

It is shown that if t ≥ 2 is rational, then there exist graphs with arbitrarily low or high edge density, bipartite graphs and oriented graphs withmean distance equal to t, and also trees and tournaments with mean distance arbitrarily close to t.Expand

We prove an asymptotically tight lower bound on the average size of independent sets in a triangle-free graph on $n$ vertices with maximum degree $d$, showing that an independent set drawn uniformly… Expand

It is shown that the largest local mean always occurs at a leaf or a vertex of degree 2 and that both cases are possible and some related results on local mean and global mean of trees are shown.Expand