The correct diameter of trivalent Cayley graphs

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Abstract

Let n be a positive integer with n≥2. The trivalent Cayley interconnection network, denoted by TCIN(n), is proposed by Vadapalli and Srimani (1995). Later, Vadapalli and Srimani (1996) claimed that the diameter of TCIN(n) is 2n−1. In this paper, we argue that the above claim is not correct. Instead, we show that the diameter of TCIN(n) is 2n−1 only for n=2 and 2n−2 for all other cases.

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This work was supported in part by the National Science Council of the Republic of China under Contract NSC 87-2213-E-009-100.

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