# The geodetic number of strong product graphs

A.P. Santhakumaran; S.V. Ullas Chandran

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 4, page 687-700
- ISSN: 2083-5892

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topA.P. Santhakumaran, and S.V. Ullas Chandran. "The geodetic number of strong product graphs." Discussiones Mathematicae Graph Theory 30.4 (2010): 687-700. <http://eudml.org/doc/270905>.

@article{A2010,

abstract = {For two vertices u and v of a connected graph G, the set $I_G[u,v]$ consists of all those vertices lying on u-v geodesics in G. Given a set S of vertices of G, the union of all sets $I_G[u,v]$ for u,v ∈ S is denoted by $I_G[S]$. A set S ⊆ V(G) is a geodetic set if $I_G[S] = V(G)$ and the minimum cardinality of a geodetic set is its geodetic number g(G) of G. Bounds for the geodetic number of strong product graphs are obtainted and for several classes improved bounds and exact values are obtained.},

author = {A.P. Santhakumaran, S.V. Ullas Chandran},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {geodetic number; extreme vertex; extreme geodesic graph; open geodetic number; double domination number},

language = {eng},

number = {4},

pages = {687-700},

title = {The geodetic number of strong product graphs},

url = {http://eudml.org/doc/270905},

volume = {30},

year = {2010},

}

TY - JOUR

AU - A.P. Santhakumaran

AU - S.V. Ullas Chandran

TI - The geodetic number of strong product graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2010

VL - 30

IS - 4

SP - 687

EP - 700

AB - For two vertices u and v of a connected graph G, the set $I_G[u,v]$ consists of all those vertices lying on u-v geodesics in G. Given a set S of vertices of G, the union of all sets $I_G[u,v]$ for u,v ∈ S is denoted by $I_G[S]$. A set S ⊆ V(G) is a geodetic set if $I_G[S] = V(G)$ and the minimum cardinality of a geodetic set is its geodetic number g(G) of G. Bounds for the geodetic number of strong product graphs are obtainted and for several classes improved bounds and exact values are obtained.

LA - eng

KW - geodetic number; extreme vertex; extreme geodesic graph; open geodetic number; double domination number

UR - http://eudml.org/doc/270905

ER -

## References

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- [6] F. Harary, E. Loukakis and C. Tsouros, The geodetic number of a graph, Mathl. Comput. Modeling 17 (1993) 89-95, doi: 10.1016/0895-7177(93)90259-2. Zbl0825.68490
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- [9] A.P. Santhakumaran and S.V. Ullas Chandran, The hull number of strong product of graphs, (communicated). Zbl1229.05240

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