Uniqueness of graph square roots of girth six

Details Uniqueness of graph square roots of girth six Uniqueness of graph square roots of girth six

2009-12-11

arxiv.org/abs/0912.2291v1

Mathematics

Combinatorics

A note, 4 pages

Scientific paper

We prove that if two graphs of girth at least 6 have isomorphic squares, then
the graphs themselves are isomorphic. This is the best possible extension of
the results of Ross and Harary on trees and the results of Farzad et al. on
graphs of girth at least 7. We also make a remark on reconstruction of graphs
from their higher powers.

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