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

• Type: Journal
• Year: 2002
• Where: ENDM
• Authors: Randall J. Elzinga, David A. Gregory, Kevin N. Vander Meulen
• Keywords: Communication Networks, Distance Matrix, ENDM 2002, Negative Eigenvalues