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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)

We introduce a generalization of the well known concept of a graceful labeling. Given a graph Γ with e = d · m edges, we call d-graceful labeling of Γ an injective function from(m + 1)}. In the case of d = 1 and of d = e we find the classical notion of a graceful labeling and of an odd graceful labeling, respectively. Also, we call d-graceful α-labeling of… (More)

- Anna Benini, Anita Pasotti
- 2014

We prove the existence of infinite classes of cyclic Γ-decompositions of the complete multipartite graph, Γ being a caterpillar, a hairy cycle or a cycle. All results are obtained by the construction of d-divisible α-labelings of Γ, introduced in [A. Pasotti, On d-graceful labelings, Ars Combin. 111 (2013), 207–223] as a generalization of classical… (More)