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On bounds for the cutting number of a graph

Author

Listed:
  • Simon Mukwembi

    (University of KwaZulu-Natal, Westville Campus)

  • Senelani Dorothy Hove-Musekwa

    (National University of Science and Technology)

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.

Suggested Citation

  • Simon Mukwembi & Senelani Dorothy Hove-Musekwa, 2012. "On bounds for the cutting number of a graph," Indian Journal of Pure and Applied Mathematics, Springer, vol. 43(6), pages 637-649, December.
    • Handle: RePEc:spr:indpam:v:43:y:2012:i:6:d:10.1007_s13226-012-0038-8
    DOI: 10.1007/s13226-012-0038-8
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    References listed on IDEAS

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    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
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