Abstract
For a given connected graph $G$ of order $n$, a routing $R$ is a set of $n(n-1)$ elementary paths specified for every ordered pair of vertices in $G$. The vertex-forwarding index $\xi(G)$ (the edge-forwarding index $\pi(G)$) of $G$ is the maximum number of paths of $R$ passing through any vertex (resp. edge) in $G$. In this paper we consider the vertex- and the edge- forwarding indices of the cartesian product of $k$ ($\ge 2$) graphs. As applications of our results, we determine the vertex- and the edge- forwarding indices of some well-known graphs, such as the $n$-dimensional generalized hypercube, the undirected toroidal graph, the directed toroidal graph and the cartesian product of the Petersen graphs.
Citation
Jun-Ming Xu. Min Xu. Xinmin Hou. "FORWARDING INDICES OF CARTESIAN PRODUCT GRAPHS." Taiwanese J. Math. 10 (5) 1305 - 1315, 2006. https://doi.org/10.11650/twjm/1500557304
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