Addressing the Petersen graph

  • Randall J. Elzingaa, David A. Gregoryb, Kevin N. Vander Meulena
  • Published 2004

Abstract

Motivated by a problem onmessage routing in communication networks, Graham and Pollak proposed a scheme for addressing the vertices of a graphGbyN-tuples of three symbols in such away that distances betweenverticesmay readily be determined from their addresses. They observed that N h(D), the maximum of the number of positive and the number of negative eigenvalues of the distance matrix D of G. A result of Gregory, Shader and Watts yields a necessary condition for equality to occur. As an illustration, we show thatN >h(D)=5 for all addressings of the Petersen graph and then give an optimal addressing by 6-tuples. © 2004 Elsevier B.V. All rights reserved.

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Cite this paper

@inproceedings{Elzingaa2004AddressingTP, title={Addressing the Petersen graph}, author={Randall J. Elzingaa and David A. Gregoryb and Kevin N. Vander Meulena}, year={2004} }