Graceful labeling in a graph consisting chord with quadrilateral snake

Graceful Tree Labeling

Graceful and odd graceful labeling of some graphs

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.

Super edge-antimagic labeling of a cycle with a chord

An (a, d)-edge-antimagic total labeling of G is a one-to-one mapping g taking the vertices and edges onto 1, 2, . . . , |V (G)| + |E(G)| so that the edgeweights w(uv) = g(u) + g(v) + g(uv), uv ∈ E(G), form an arithmetic progression with initial term a and common difference d. Such a labeling is called super if the smallest labels appear on the vertices. In this paper, we investigate the existen...

Vertex Equitable Labeling of Double Alternate Snake Graphs

Let G be a graph with p vertices and q edges and A = {0, 1, 2, . . . , [q/2]}. A vertex labeling f : V (G) → A induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. For a ∈ A, let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |vf (a) − vf (b)| ≤ 1 and the indu...

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...