Anita Pasotti

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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)
J.A. Gallian has proved [J.A. Gallian, Labeling prisms and prism related graphs, Congr. Numer. 59 (1987) 89–100] that every cubic graphM2k obtainable from a 2k-cycle by adding its k diameters (the so-calledMoebius Ladder of order 2k) is graceful. Here, in the case of k even, we propose a new graceful labeling that besides being simpler than Gallian’s one is(More)
(a, b, c, d) r{1, 2, 3, 5} (0, 2v + 4, 1, 2) [0, . . . , 2v, 2v + 5, 2v + 7, 2v + 2, 2v + 4, 2v + 6, 2v + 3, . . . , 1] (0, 2v + 5, 1, 2) [0, . . . , 2v + 4, 2v + 7, 2v + 5, 2v + 3, 2v + 8, 2v + 6, 2v + 1, . . . , 1] (0, 2v + 3, 2, 1) [0, . . . , 2v, 2v + 5, 2v + 2, 2v + 4, 2v + 6, 2v + 3, . . . , 1] (0, 2v + 4, 2, 1) [0, . . . , 2v + 2, 2v + 7, 2v + 5, 2v(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({1a, 2b, tc}) 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)