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...

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...

A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by χ=(G). It is interesting to note that if a graph G is equitably k-colorable, it does not imply that it is equitab...

A total vertex irregular k-labeling φ of a graph G is a labeling of the vertices and edges of G with labels from the set {1, 2, . . . , k} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x. The minimum k for which the graph G...