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arXiv · 1609.05995

Addressing Graph Products and Distance-Regular Graphs

Sebastian M. Cioabă·Randall J. Elzinga·Michelle Markiewitz·Kevin Vander Meulen·Trevor Vanderwoerd
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Abstract

Graham and Pollak showed that the vertices of any connected graph $G$ can be assigned $t$-tuples with entries in $\{0, a, b\}$, called addresses, such that the distance in $G$ between any two vertices equals the number of positions in their addresses where one of the addresses equals $a$ and the other equals $b$. In this paper, we are interested in determining the minimum value of such $t$ 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.

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Sebastian M. Cioabă, Randall J. Elzinga, Michelle Markiewitz, Kevin Vander Meulen, Trevor Vanderwoerd. 2016-09-20. Addressing Graph Products and Distance-Regular Graphs. https://arxiv.org/abs/1609.05995

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