We show that to each graceful labelling of a path on 2s + 1 vertices, s ≥ 2, there corresponds a current assignment on a 3-valent graph which generates at least 22s cyclic oriented triangular embeddings of a complete graph on 12s + 7 vertices. We also show that in this correspondence, two distinct graceful labellings never give isomorphic oriented embeddings. Since the number of graceful labell...

An odd graceful labeling of a graph ( , ) G V E = is a function : ( ) {0,1,2, . . .2 ( ) 1} f V G E G → − such that | ( ) ( )| f u f v − is odd value less than or equal to 2 ( ) 1 E G − for any , ( ) u v V G ∈ . In spite of the large number of papers published on the subject of graph labeling, there are few algorithms to be used by researchers to gracefully label graphs. This work provides gene...

Let be a connected graph with vertex set and edge . The bijective function is said to labeling of where the associated weight for If every has different weight, called an antimagic labeling. A path in vertex-labeled , two edges satisfies rainbow path. if vertices there exists Graph admits coloring, we assign each color smallest number colors induced from all weights connection denoted by In thi...

1 Abstract Standard representations of irregular nite element meshes combine vertex data sample coordinates and node values and connectivity tetrahedron-vertex incidence. Connectivity speciies how the samples should be interpolated. It may beencoded for each tetrahedron as four vertex-references,

A graph with p vertices and q edges is said to have an even vertex odd mean labeling if there exists an injective function f:V(G){0, 2, 4, ... 2q-2,2q} such that the induced map f*: E(G) {1, 3, 5, ... 2q-1} defined by f*(uv)=     f u f v 2  is a bijection. A graph that admits an even vertex odd mean labeling is called an even vertex odd mean graph. In this paper we pay our attention to p...

Let G be a graph with p vertices and q edges and let = 0,1, 2, , . 2 q A              A vertex labeling   : f V G A  i e a vertex equitable labeling of G if it induces an edge labeling s said to b given by      * =  f uv f u f v  * f such that     1 v a v b   and     * = 1,2,3, , f f f E q  , where   f v a is the ber of verti num ces v with   = f v a for . ...

Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of graphs the precise values of these parameters are proved. © 2006 Elsevier B.V. All rights reserved.