Addressing Graph Products and Distance-Regular Graphs
Combinatorics
2017-01-04 v2 Discrete Mathematics
Abstract
Graham and Pollak showed that the vertices of any connected graph can be assigned -tuples with entries in , called addresses, such that the distance in between any two vertices equals the number of positions in their addresses where one of the addresses equals and the other equals . In this paper, we are interested in determining the minimum value of such for various families of graphs. We develop two ways to obtain this value for the Hamming graphs and present a lower bound for the triangular graphs.
Keywords
Cite
@article{arxiv.1609.05995,
title = {Addressing Graph Products and Distance-Regular Graphs},
author = {Sebastian M. Cioabă and Randall J. Elzinga and Michelle Markiewitz and Kevin Vander Meulen and Trevor Vanderwoerd},
journal= {arXiv preprint arXiv:1609.05995},
year = {2017}
}
Comments
10 pages, 2 figures; This version is identical to the first in content, but it includes more explicit attributions to David A. Gregory. In particular, for Lemmas 3.1, 3.2, Remark 3.4 and Theorem 3.5 and includes an added acknowledgement