Products of Geodesic Graphs and the Geodetic Number of Products

Jake A. Soloff, Rommy A. Márquez, and Louis M. Friedler. "Products of Geodesic Graphs and the Geodetic Number of Products." Discussiones Mathematicae Graph Theory 35.1 (2015): 35-42. <http://eudml.org/doc/271222>.

@article{JakeA2015,
abstract = {Given a connected graph and a vertex x ∈ V (G), the geodesic graph Px(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 Km,n with itself, where m, n ≥ 4, is equal to the minimum of m, n and eight.},
author = {Jake A. Soloff, Rommy A. Márquez, Louis M. Friedler},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {geodesic graph; geodetic number; Cartesian products},
language = {eng},
number = {1},
pages = {35-42},
title = {Products of Geodesic Graphs and the Geodetic Number of Products},
url = {http://eudml.org/doc/271222},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Jake A. Soloff
AU - Rommy A. Márquez
AU - Louis M. Friedler
TI - Products of Geodesic Graphs and the Geodetic Number of Products
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 1
SP - 35
EP - 42
AB - Given a connected graph and a vertex x ∈ V (G), the geodesic graph Px(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 Km,n with itself, where m, n ≥ 4, is equal to the minimum of m, n and eight.
LA - eng
KW - geodesic graph; geodetic number; Cartesian products
UR - http://eudml.org/doc/271222
ER -