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The size of a (v, 5, 2, 1) optical orthogonal code (OOC) is shown to be at most equal to v 12 when v ≡ 11 (mod 132) or v ≡ 154 (mod 924), and at most equal to v 12 in all the other cases. Thus a (v, 5, 2, 1)-OOC is naturally said to be optimal when its size reaches the above bound. Many direct and recursive constructions for infinite classes of optimal (v,… (More)

We report in the following tables a linear realization of some lists L = {1 a , 2 b , 3 c , 5 d } used by the authors to prove the results of [1], omitted there for sake of brevity. We order the lists according to the Lemmas/Propositions/Theorems in which they are used. In the second column of the following tables, we write P if the corresponding linear… (More)

In this paper we investigate a problem proposed by Marco Buratti, Peter Horak and Alex Rosa (denoted by BHR-problem) concerning Hamiltonian paths in the complete graph with prescribed edge-lengths. In particular we solve BHR({1 a , 2 b , t c }) for any even integer t 4, provided that a+b t−1. Furthermore, for t = 4, 6, 8 we present a complete solution of… (More)

An α-labeling of a bipartite graph Γ of size e is an injective function and with the property that its maximum value on one of the two bipartite sets does not reach its minimum on the other one. We prove that the generalized Petersen graph P 8n,3 admits an α-labeling for any integer n ≥ 1 confirming that the conjecture posed by Vietri in [10] is true. In… (More)