Elsevier

Discrete Mathematics

Volume 338, Issue 12, 6 December 2015, Pages 2412-2420
Discrete Mathematics

Centralization of transmission in networks

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Abstract

Freeman’s centralization (Freeman, 1978) for a given centrality index is a measure of how central a vertex is regarding to how central all the other vertices are with respect to the given index. The transmission of a vertex v in a graph G is equal to the sum of distances between v and all other vertices of G. In this paper we study the centralization of transmission, in particular, we determine the graphs on n vertices which attain the maximum or minimum value. Roughly, the maximizing graphs are comprised of a path which has one end glued to a clique of similar order. The minimizing family of extremal graphs consists of three paths of almost the same length, glued together in one end-vertex. We conclude the paper with some problems for possible further work.

Keywords

Extremal graphs
Transmission
Freeman centralization
Centrality
Wiener index

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