On Graceful Digraphs

نویسنده

  • S. M. Hegde
چکیده

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 digraph have? In this paper, we give an upper bound for the distinct graceful labeling of unidirectional cycle −→ Cn.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Further Results on Graceful Digraphs

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 digra...

متن کامل

A 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 کامل

More 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 کامل

Constructing 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 کامل

On spectral radius of strongly connected digraphs

 It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.  

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011