Further Results on Graceful Digraphs
نویسنده
چکیده
A digraph D with p vertices and q arcs is labeled by assigning a distinct integer value g(v) from {0, 1, ..., q} to each vertex v. The vertex values, in turn, induce a value g(u, v) on each arc (u, v) where g(u, v) = (g(v)− g(u))(mod q + 1). If the arc values are all distinct then the labeling is called a graceful labeling of a digraph. In this paper, we prove a general result on graceful digraphs of which Du and Sun’s conjecture (J. Beijing Univ. Posts Telecommun, 17: 85–88 1994) is a special case. Further, we provide an upper bound for the number of non isomorphic graceful directed cycles obtained from a graceful labeling of the unicycle −→ Cn .
منابع مشابه
On Graceful Digraphs
In 1994, Du and Sun conjectured that, for any positive even n and any integer m, the digraph n. −→ Cm is graceful. In this paper we prove the conjecture. Also, in 1985, Bloom and Hsu mentioned that the question remains open for the non generalized graceful labelings. For example, the following question is currently unanswered: How many distinct graceful labelings does a designated graceful digr...
متن کاملA Survey of the Gracefulness of Digraphs
Graph labeling traces its origin to the famous conjecture that all trees are graceful presented by A.Rosa in 1966. In recent years, many research papers on graceful graph have been published. In this survey we have collected studies on the gracefulness of the directed circuit ~ Cm and the union graph of mutually non-intersecting ~ Cm, the digraph n · ~ Cm, the digraph n − ~ Cm, the union of the...
متن کاملMore skew-equienergetic digraphs
Two digraphs of same order are said to be skew-equienergetic if their skew energies are equal. One of the open problems proposed by Li and Lian was to construct non-cospectral skew-equienergetic digraphs on n vertices. Recently this problem was solved by Ramane et al. In this paper, we give some new methods to construct new skew-equienergetic digraphs.
متن کاملConstructing Graceful Graphs with Caterpillars
A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. If a graceful labeling f of a bipartite graph G assigns the smaller labels to one of the two stable sets of G, then f ...
متن کاملSufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs
Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree and its in-degree . Now let D be a digraph with minimum degree and edge-connectivity If is real number, then the zeroth-order general Randic index is defined by . A digraph is maximally edge-connected if . In this paper we present sufficient condi...
متن کامل