A vertex (edge) irregular total k-labeling ? of a graph G is labeling the vertices and edges with labels from set {1,2,...,k} in such way that any two different (edges) have distinct weights. Here, weight x sum label all incident x, whereas an edge to edge. The minimum k for which has called irregularity strength G. In this paper, we are dealing infinite classes convex polytopes generated by pr...

Radio labeling is derived from the assignment of radio frequencies (channels) to a set of transmitters. The frequencies assigned depend on the geographical distance between the transmitters: the closer two transmitters are, the greater the potential for interference between their signals. Thus when the distance between two transmitters is small, the difference in the frequencies assigned must b...

The local antimagic total vertex labeling of graph G is a that every vertices and edges label by natural number from 1 to such two adjacent has different weights, where sum the labels all incident vertex. If start smallest then edge so kind coloring called super labeling. That induces for v, weight w(v) color v. minimum colors obtained chromatic G, denoted χlsat(G). In this paper, we consider G...

The problem of deciding whether two graphs are isomorphic is fundamental in graph theory. Moreover, the flexibility with which other combinatorial objects can be modeled by graphs has meant that efficient programs for deciding whether graphs are isomorphic have also been used to study a variety of other combinatorial structures. Not only is the graph isomorphism problem a very practical one, it...

The Graceful Tree Conjecture claims that every finite simple tree of order n can be vertex labeled with integers {1, 2, ...n} so that the absolute values of the differences of the vertex labels of the end-vertices of edges are all distinct. That is, a graceful labeling of a tree is a vertex labeling f , a bijection f : V (Tn) −→ {1, 2, ...n}, that induces an edge labeling g(uv) = |f(u)− f(v)| t...

If the vertex set V of > =< V,E G can be divided into two un empty sets X and Y , ∅ = = Y V,X Y X ∩ ∪ , but also two nodes of every edge belong to X and Y separately, the G is called bipartite graph. If E ) ,y Y,(x X,y x i i i i ∈ ∈ ∈ ∀ then G is called complete bipartite graph. if n Y m, X = = , the G is marked m,n K . In this paper the graceful labeling, k-graceful labeling, odd graceful labe...

A graph G on m edges is considered graceful if there is a labelling f of the vertices of G with distinct integers in the set {0, 1, . . . ,m} such that the induced edge labelling g defined by g(uv) = |f(u) − f(v)| is a bijection to {1, . . . ,m}. We here consider some relaxations of these conditions as applied to tree labellings: 1. Edge-relaxed graceful labellings, in which repeated edge label...

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...

This papers deals with the Edge cordial labeling of newly introduced eight sprocket graph. graph is already proven as and gracious in labelling. In our study we have further proved that Eight Sprocket related families connected edge-cordial graphs. Also path union graph, cycle star are Edge-cordial.Â

A graph that admits a Smarandachely near mean m-labeling is called Smarandachely near m-mean graph. The graph that admits a near mean labeling is called a near mean graph (NMG). In this paper, we proved that the graphs Pn, Cn,K2,n are near mean graphs and Kn(n > 4) and K1,n(n > 4) are not near mean graphs.