Geodesic Graphoidal Covering Number of a Graph

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Authors

  • Arulmigu Kalasalingam College o f Engineering, Krishnankoil-626 190 ,IN
  • Department of Mathematics, St. John's College Tirunelveli-627 002 ,IN

Keywords:

Graphoidal Cover, Acyclic Graphoidal Cover, Geodcsic Graphoidal Cover.

Abstract

A geodesic graphical cover of a graph G is a collection ψ of shortest paths in G such that every path in ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in ψ and every edge of G is in exactly one path in ψ. The minimum cardinality of a geodesic graphical cover of G is called the geodesic graphical covering number of G and is denoted by ηg. In this paper, we determine ηg for several classes of graphs. We also prove that ηg≥[q/d(G)] where d(G) is the diameter of G and characterize some classes o f graphs which attain this bound.

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Published

2005-12-01

How to Cite

Arumugam, S., & Suresh Suseela, J. (2005). Geodesic Graphoidal Covering Number of a Graph. The Journal of the Indian Mathematical Society, 72(1-4), 99–106. Retrieved from https://informaticsjournals.com/index.php/jims/article/view/21821