Addressing the Petersen graph
نویسندگان
چکیده
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
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 286 شماره
صفحات -
تاریخ انتشار 2002