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THE ORIENTABLE NUMBERS OF A GRAPH
THE ORIENTABLE NUMBERS OF A GRAPH
Journal of applied mathematics & informatics. 2014. May, 32(3_4): 503-509
  • Received : November 05, 2013
  • Published : May 30, 2014
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Kim Byung Kee

Abstract
For a connected graph G, there are orientations of G have different hull numbers, geodetic numbers, and convexity numbers. The lower orientable hull number <TEX>$h^-(G)$</TEX> is defined as the minimum hull number among all the orientations of G and the upper orientable hull number <TEX>$h^+(G)$</TEX> as the maximum hull number among all the orientations of G. The lower and upper orientable geodetic numbers <TEX>$g^-(G)$</TEX> and <TEX>$g^+(G)$</TEX> are defined similarily. In this paper, We investigate characterizations of the orientable numbers and the conditions that the relation <TEX>$h^-(G){\leq}g^-(G)$</TEX> < <TEX>$h^+(G){\leq}g^+(G)$</TEX> holds.
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