Missing Numbers in -Graceful Graphs
نویسندگان
چکیده
The generalization of graceful labeling is termed as -graceful labeling. In this paper it has been shown that , is -graceful for any (set of natural numbers) and some results related to missing numbers for -graceful labeling of cycle , comb , hairy cycle and wheel graph have been discussed.
منابع مشابه
Graceful labelings of the generalized Petersen graphs
A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...
متن کاملSnakes 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 کاملOn Topological Numbers of Graphs
This paper introduces the notion of discrete t-set graceful graphs and obtains some of their properties. It also examines the interrelations among different types of set-indexers, namely, set-graceful, set-semigraceful, topologically set-graceful (t-set graceful), strongly t-set graceful and discrete t-set graceful and establishes how all these notions are interdependent or not. AMS Mathematics...
متن کاملSuper-edge-graceful labelings of multi-level wheel graphs, fan graphs and actinia graphs
graceful labeling of G. Such sets P and Q are called the vertex values set and edge labels set of G, respectively. The notions of super-edge-graceful graphs and edge-graceful graphs are different. Mitchem and Simoson [6] showed that the step graph C2 6 is super-edge-graceful but not edge-graceful. Shiu [7] showed that the complete graph K4 is edge-graceful but not super-edge-graceful. Mitchem a...
متن کامل