Transmission in Certain Trees.

Transmission of a vertex u in a graph G is defined as T(u) = ∑ v∈V(G) d(u,v) [1]. The expression T(G) = 1/2∑ u,v∈V(G) d(u,v) is called the transmission of G. Further the cardinality of the set {T(u)/u ∈ V(G)} is addressed as the transmission dimension of G and is denoted by dim T (G) [5]. Closeness centrality of a vertex v in G is defined as the reciprocal of the transmission of v. Using this centrality measure, the most important vertices in the graph are identified. In this paper we have computed the transmission of every vertex of an r -regular caterpillar and a spanning tree of the hypercube network. [ABSTRACT FROM AUTHOR]