Many graph search algorithms use a labeling of the vertices to compute an ordering of the vertices. We generalize this idea by devising a general vertex labeling algorithmic process called General Label Search (GLS), which uses a labeling structure which, when specified, defines specific algorithms. We characterize the vertex orderings computable by the basic types of searches in terms of prope...

In this paper we study the problem of labeling the edges of a graph with positive integers such that the sequence of the sums of incident edges of each vertex makes a finite arithmetic progression. We give conditions for paths, cycles, and bipartite graphs to have such a labeling. We then address the opposite problem of finding an edge labeled graph for a given finite arithmetic progression. We...

We discuss coloring and partitioning questions related to Sperner’s Lemma, originally motivated by an application in hardness of approximation. Informally, we call a partitioning of the (k − 1)-dimensional simplex into k parts, or a labeling of a lattice inside the simplex by k colors, “Sperner-admissible” if color i avoids the face opposite to vertex i. The questions we study are of the follow...

This paper introduces the notion of informative labeling schemes for arbitrary graphs. Let f (W) be a function on subsets of vertices W . An f labeling scheme labels the vertices of a weighted graph G in such a way that f (W) can be inferred (or at least approximated) efficiently for any vertex subset W of G by merely inspecting the labels of the vertices of W, without having to use any additio...

For example is a chromatic number with the smallest integer so that graph has true vertex coloring k color. Chromatic still an interesting study which being studied for its development through coloring. Graph special case of labeling. Labeling here means, giving color to points at certain limit no two vertices have same This aims calculate in several classes graphs including , Based on results ...