For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x,y in G there exist vertices u,v ∈ S such that x,y ∈ I[u,v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic of cardinality dg(G) is called dg-set of G. The double geodetic numbers of certain standard graphs are obtained. It is shown that for positive integers r,d such that r < d ≤ 2r and 3 ≤ a ≤ b there exists a connected graph G with rad G = r, diam G = d, g(G) = a and dg(G) = b. Also, it is proved that for integers n, d ≥ 2 and l such that 3 ≤ k ≤ l ≤ n and n-d-l+1 ≥ 0, there exists a graph G of order n diameter d, g(G) = k and dg(G) = l.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1589,
author = {A.P. Santhakumaran and T. Jebaraj},
title = {Double geodetic number of a graph},
journal = {Discussiones Mathematicae Graph Theory},
volume = {32},
year = {2012},
pages = {109-119},
zbl = {1255.05069},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1589}
}
A.P. Santhakumaran; T. Jebaraj. Double geodetic number of a graph. Discussiones Mathematicae Graph Theory, Tome 32 (2012) pp. 109-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1589/
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