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Edge geodetic number of a graph. (English) Zbl 1133.05028

An edge geodetic cover of a graph \(G=(V,E)\) is a subset \(S\) of \(V\) such that every edge of \(G\) is contained in a shortest path joining some pair of vertices in \(S\). The edge geodetic number of \(G\) is the minimum order of its edge geodetic covers. The authors give various properties of the edge geodetic number; some of them relate to other parameters such as radius, diameter, and the (vertex) geodetic number.

MSC:

05C12 Distance in graphs
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References:

[1] Buckley F., Distance in Graphs (1990) · Zbl 0688.05017
[2] Buckley F., Scientia 2 pp 17– (1988)
[3] Chartrand G., Networks 39 (1) pp 1– (2002) · Zbl 0987.05047 · doi:10.1002/net.10007
[4] Chartrand G., Discrete Mathematics 242 pp 41– (2002) · Zbl 0988.05034 · doi:10.1016/S0012-365X(00)00456-8
[5] Ostrand P. A., Discrete Mathematics 4 pp 71– (1973) · Zbl 0265.05123 · doi:10.1016/0012-365X(73)90116-7
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