Double geodetic number of a graph

A.P. Santhakumaran, and T. Jebaraj. "Double geodetic number of a graph." Discussiones Mathematicae Graph Theory 32.1 (2012): 109-119. <http://eudml.org/doc/270828>.

@article{A2012,
abstract = {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.},
author = {A.P. Santhakumaran, T. Jebaraj},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {geodetic number; weak-extreme vertex; double geodetic set; double geodetic number},
language = {eng},
number = {1},
pages = {109-119},
title = {Double geodetic number of a graph},
url = {http://eudml.org/doc/270828},
volume = {32},
year = {2012},
}

TY - JOUR
AU - A.P. Santhakumaran
AU - T. Jebaraj
TI - Double geodetic number of a graph
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 1
SP - 109
EP - 119
AB - 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.
LA - eng
KW - geodetic number; weak-extreme vertex; double geodetic set; double geodetic number
UR - http://eudml.org/doc/270828
ER -