Some Results on Strong Edge Geodetic Problem in Graphs

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 geodeti...

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Bibliographic Details
Published in:Communications in Mathematics and Applications 2020-01, Vol.11 (3), p.403
Main Authors: D. Antony Xavier, Mathew, Deepa, Santiagu Theresal, Eddith Sarah Varghese
Format: Article
Language:English
Subjects:
Apexes
Graph theory
Graphs
Mathematics
Online Access:Get full text
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Summary: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.
ISSN:0976-5905
0975-8607
DOI:10.26713/cma.v11i3.1385