ArticleOriginal scientific text
Title
The edge geodetic number and Cartesian product of graphs
Authors 1, 1
Affiliations
- Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai - 627 002, India
Abstract
For a nontrivial connected graph G = (V(G),E(G)), a set S⊆ V(G) is called an edge geodetic set of G if every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g₁(G) of G is the minimum order of its edge geodetic sets. Bounds for the edge geodetic number of Cartesian product graphs are proved and improved upper bounds are determined for a special class of graphs. Exact values of the edge geodetic number of Cartesian product are obtained for several classes of graphs. Also we obtain a necessary condition of G for which g₁(G ☐ K₂) = g₁(G).
Keywords
geodetic number, edge geodetic number, linear edge geodetic set, perfect edge geodetic set, (edge, vertex)-geodetic set, superior edge geodetic set
Bibliography
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Pages:
55-73
Main language of publication
English
Received
2008-05-28
Accepted
2008-12-11
Published
2010
DOI: 10.7151/dmgt.1476
Exact and natural sciences