Abstract
For a nontrivial connected graph \(G=(V(G),E(G)),\) a set \(S\subseteq V(G)\) 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 eg(G) of G is the minimum order of its edge geodetic sets. It is observed that the edge geodetic sets and numbers are interesting concepts and possess properties distinct from the vertex geodetic concepts. In this work, we determine some bounds and exact values of the edge geodetic numbers of strong and lexicographic products of graphs.
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Anand, B.S., Changat, M., Ullas Chandran, S.V. (2018). The Edge Geodetic Number of Product Graphs. In: Panda, B., Goswami, P. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2018. Lecture Notes in Computer Science(), vol 10743. Springer, Cham. https://doi.org/10.1007/978-3-319-74180-2_12
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DOI: https://doi.org/10.1007/978-3-319-74180-2_12
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