On Odd-graceful Labeling of Disjoint Union of Graphs

نویسندگان

  • AYESHA RIASAT
  • SALMA KANWAL
  • SANA JAVED
  • Abdus Salam
چکیده

Let G = (V, E) be a finite, simple and undirected graph having v = |V (G)| and e = |E(G)|. A graph G with q edges is said to be odd-graceful if there is an injection f : V (G) → {0, 1, 2, . . . , 2q−1} such that, when each edge xy is assigned the label |f(x)−f(y)|, the resulting edge labels are {1, 3, 5, . . . , 2q−1}. Motivated by the work of Z. Gao [6], we have defined odd graceful labeling for some other union of graphs. In this paper we formulate odd-graceful labeling for disjoint unions of graphs consisting of generalized combs, ladder, star, bistar, caterpillar and path.

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

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

Variation of Graceful Labeling on Disjoint Union of two Subdivided Shell Graphs

A shell graph is the join of a path P k of 'k' vertices and K 1. A subdivided shell graph can be constructed by subdividing the edges in the path of the shell graph. In this paper we prove that the disjoint union of two subdivided shell graphs is odd graceful and also one modulo three graceful. 1. Introduction A graph labeling is an assignment of integers to the vertices or edges, or both, subj...

متن کامل

Three Graceful Operations

A graph of size n is said to be graceful when is possible toassign distinct integers from {0, 1, . . . , n} to its verticesand {|f(u)−f(v)| : uv ∈ E(G)} consists of n integers. Inthis paper we present broader families of graceful graphs; these families are obtained via three different operations: the third power of a caterpillar, the symmetric product of G and K2 , and the disjoint union of G a...

متن کامل

Odd Graceful Labeling of Acyclic Graphs

Let G = (V, E) be a finite, simple and undirected graph. A graph G with q edges is said to be odd-graceful if there is an injection f : V (G) → {0, 1, 2, . . . , 2q− 1} such that, when each edge xy is assigned the label |f (x)− f (y)| , the resulting edge labels are {1, 3, 5, . . . , 2q− 1} and f is called an odd graceful labeling of G. Motivated by the work of Z. Gao [6] in which he studied th...

متن کامل

Snakes and Caterpillars in Graceful Graphs

Graceful labelings use a prominent place among difference vertex labelings. In this work we present new families of graceful graphs all of them obtained applying a general substitution result. This substitution is applied here to replace some paths with some trees with a more complex structures. Two caterpillars with the same size are said to be textit{analogous} if thelarger stable sets, in bo...

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 2012