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ENDM
2002

Addressing the Petersen graph

13 years 11 months ago
Addressing the Petersen graph
Motivated by a problem on message routing in communication networks, Graham and Pollak proposed a scheme for addressing the vertices of a graph G by N-tuples of three symbols in such a way that distances between vertices may 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 that N > h(D) = 5 for all addressings of the Petersen graph and then give an optimal addressing by 6-tuples. MSC: 05C50, 05C20
Randall J. Elzinga, David A. Gregory, Kevin N. Van
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2002
Where ENDM
Authors Randall J. Elzinga, David A. Gregory, Kevin N. Vander Meulen
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