Graceful and odd graceful labeling of some graphs
نویسنده
چکیده
In this paper, we prove that the square graph of bistar Bn,n, the splitting graph of Bn,n and the splitting graph of star K1,n are graceful graphs. We also prove that the splitting graph and the shadow graph of bistar Bn,n admit odd graceful labeling.
منابع مشابه
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 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 کاملNew Families of Odd Graceful Graphs
In this work some new odd graceful graphs are investigated. We prove that the graph obtained by fusing all the n vertices of Cn of even order with the apex vertices of n copies of K1,m admits odd graceful labeling. In addition to this we show that the shadow graphs of path Pn and star K1,n are odd graceful graphs.
متن کاملOdd Gracefull Labeling for the Subdivison of Double Triangles Graphs
The aim of this paper is to present some odd graceful graphs. In particular we show that an odd graceful labeling of the all subdivision of double triangular snakes ( 2 k ∆ -snake ). We also prove that the all subdivision of 2 1 m∆ -snake are odd graceful. Finally, we generalize the above two results (the all subdivision of 2 k m∆ -snake are odd graceful).
متن کاملImproper Graceful and Odd-graceful Labellings of Graph Theory
Abstract In this paper we define some new labellings for trees, called the in-improper and out-improper odd-graceful labellings such that some trees labelled with the new labellings can induce graceful graphs having at least a cycle. We, next, apply the new labellings to construct large scale of graphs having improper graceful/odd-graceful labellings or having graceful/odd-graceful labellings.
متن کامل