Products of Geodesic Graphs and the Geodetic Number of Products
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 35-42
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Given a connected graph and a vertex x ∈ V (G), the geodesic graph P_x(G) has the same vertex set as G with edges uv iff either v is on an x − u geodesic path or u is on an x − v geodesic path. A characterization is given of those graphs all of whose geodesic graphs are complete bipartite. It is also shown that the geodetic number of the Cartesian product of K_m,n with itself, where m, n ≥ 4, is equal to the minimum of m, n and eight.
Keywords:
geodesic graph, geodetic number, Cartesian products
@article{DMGT_2015_35_1_a2,
author = {Soloff, Jake A. and M\'arquez, Rommy A. and Friedler, Louis M.},
title = {Products of {Geodesic} {Graphs} and the {Geodetic} {Number} of {Products}},
journal = {Discussiones Mathematicae. Graph Theory},
pages = {35--42},
publisher = {mathdoc},
volume = {35},
number = {1},
year = {2015},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a2/}
}
TY - JOUR AU - Soloff, Jake A. AU - Márquez, Rommy A. AU - Friedler, Louis M. TI - Products of Geodesic Graphs and the Geodetic Number of Products JO - Discussiones Mathematicae. Graph Theory PY - 2015 SP - 35 EP - 42 VL - 35 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a2/ LA - en ID - DMGT_2015_35_1_a2 ER -
%0 Journal Article %A Soloff, Jake A. %A Márquez, Rommy A. %A Friedler, Louis M. %T Products of Geodesic Graphs and the Geodetic Number of Products %J Discussiones Mathematicae. Graph Theory %D 2015 %P 35-42 %V 35 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a2/ %G en %F DMGT_2015_35_1_a2
Soloff, Jake A.; Márquez, Rommy A.; Friedler, Louis M. Products of Geodesic Graphs and the Geodetic Number of Products. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 35-42. http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a2/