1 research outputs found
Nonmedian Direct Products of Graphs with Loops
A \emph{median graph} is a connected graph in which, for every three
vertices, there exists a unique vertex lying on the geodesic between any
two of the given vertices. We show that the only median graphs of the direct
product are formed when , for any integer and
, for any integer , with a loop at an end vertex, where the
direct product is taken over all connected graphs on at least three
vertices or at least two vertices with at least one loop, and connected graphs
with at least one loop.Comment: Accepted to Ars Combinatoria (August 25, 2010