Let ( , ) G V E be a simple graph. For a total labeling { } : 1,2,3,..., V E k ∂ ∪ → the weight of a vertex x is defined as ( ) ( ) ( ). xy E wt x x xy ∈ = ∂ + ∂ ∑ ∂ is called a vertex irregular total k-labeling if for every pair of distinct vertices x and y, ( ) ( ). wt x wt y ≠ . The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularit...

A vertex-irregular total k-labelling λ : V (G)∪E(G) −→ {1, 2, ..., k} of a graph G is a labelling of vertices and edges of G in such a way that for any different vertices x and y, their weights wt(x) and wt(y) are distinct. The weight wt(x) of a vertex x is the sum of the label of x and the labels of all edges incident with x. The minimum k for which a graph G has a vertex-irregular total k-lab...

In this paper we present a data-parallel language called MPL, for which the basic data structure is the graph. The purpose of this language is to program numerical algorithms that use irregular data, and to allow them to execute on distributed memory MIMD machines. We deene the graph data structure and give some examples of how irregular data structures can be described from graphs with our app...

An edge irregular total k-labeling of a graph G is a labeling of the vertices and edges with labels 1, 2, . . . , k such that the weights of any two different edges are distinct, where the weight of an edge is the sum of the label of the edge itself and the labels of its two end vertices. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregul...

Ebert, G., J. Hemmeter, F. Lazebnik and A. Woldar, On the number of irregular assignments on a graph, Discrete Mathematics 93 (1991) 131-142. Let G be a simple graph which has no connected components isomorphic to K, or K,, and let Z+ be the set of positive integers. A function o: E(G)-,Z+ is called an assignment on G, and for an edge e of G, w(e) is called the weight of e. We say that o is of ...

A graph is locally irregular if any pair of adjacent vertices have distinct degrees. decomposition a G D such that every subgraph H∈D irregular. said to be decomposable it admits decomposition. We prove split can decomposed into at most three subgraphs and we characterize all graphs whose one, two or subgraphs.

An assignment of positive integer weights to the edges of a simple graph G is called irregular if the weighted degrees of the vertices are all different. The irregularity strength, s(G), is the maximal edge weight, minimized over all irregular assignments, and is set to infinity if no such assignment is possible. In this paper, we take an iterative approach to calculating the irregularity stren...

An edge irregular total k-labeling of a graph G = (V,E) is a labeling φ : V ∪ E → {1, 2, . . . , k} such that the total edge-weights wt(xy) = φ(x) + φ(xy) + φ(y) are different for all pairs of distinct edges. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G. In this paper, we determined the exact values of the total e...

RAPID is a run-time system that uses an inspector/executor approach to parallelize irregular computations by embodying graph scheduling techniques to optimize interleaved communication and computation with mixed granularities. It provides a set of library functions for specifying irregular data objects and tasks that access these objects, extracts a task dependence graph from data access patter...