On bounds for the cutting number of a graph

Simon Mukwembi () and Senelani Dorothy Hove-Musekwa
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Simon Mukwembi: University of KwaZulu-Natal, Westville Campus
Senelani Dorothy Hove-Musekwa: National University of Science and Technology

Indian Journal of Pure and Applied Mathematics, 2012, vol. 43, issue 6, 637-649

Abstract: Abstract The cutting number of a vertex v of a finite graph G = (V,E) is a natural measure of the extent to which the removal of v disconnects the graph. Precisely, the cutting number c(v) of v is defined as the number of pairs of vertices {u,w} of G such that u,w ≠ v and every u-w path contains v. The cutting number c(G) of G is the maximum value of c(v) over all vertices in V. We provide exact bounds on the cutting number of G in terms of order and diameter of the graph.

Keywords: Network; centrality; graph; cutting number; diameter (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s13226-012-0038-8

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