Advances and Applications in Discrete Mathematics
Volume 13, Issue 1, Pages 9 - 22
(January 2014)
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SPLIT GEODETIC NUMBER OF A GRAPH
Venkanagouda M. Goudar, Ashalatha K. S. and Venkatesha
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Abstract: Let G be a graph. If then a geodesic of G is the shortest path between u and v. The closed interval consists of all vertices lying in some geodesic of G. For the set is the union of all sets for A set S is a geodetic set of G if The cardinality of a minimum geodetic set of G is the geodetic number of G, denoted by In this paper, we study the split geodetic number of a graph. is a split geodetic set in G if S is a geodetic set and is disconnected, split geodetic number of G is the minimum cardinality of a split geodetic set of G. We investigate the relationship between split geodetic number and geodetic number. We also obtain the split geodetic number in the Cartesian product of graphs. |
Keywords and phrases: Cartesian product, distance, edge covering number, split geodetic number, vertex covering number. |
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