Some Results on Strong Edge Geodetic Problem in Graphs

D. Antony Xavier, Deepa Mathew, Santiagu Theresal, Eddith Sarah Varghese

Abstract


For a graph \(G(V(G),E(G))\), the problem to find a \(S\subseteq V(G)\) where every edge of the graph \(G\) is covered by a unique fixed geodesic between the pair of vertices in \(S\) is called the strong edge geodetic problem and the cardinality of the smallest such \(S\) is the strong edge geodetic number of \(G\). In this paper the strong edge geodetic problem for product graphs are studied and also some results for general graphs are derived.


Keywords


Strong edge geodetic number; Strong geodetic number; Edge geodetic number; Geodetic set

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v11i3.1385

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