For a given simple graph an average labelling is de)ned. The graphs with average labellings and all the admissible average labellings for such graphs are characterized. c © 2001 Elsevier Science B.V. All rights reserved.

Assume that we have m identical graphs where the graphs consists of paths with k vertices where k is a positive integer. In this paper, we discuss certain labelling of the m graphs called c-Erdösian for some positive integers c. We regard labellings of the vertices of the graphs by positive integers, which induce the edge labels for the paths as the sum of the two incident vertex labels. They h...

A graph is called degree-magic if it admits a labelling of the edges by integers 1, 2, . . . , |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to 1+|E(G)| 2 deg(v). Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.

The (d,1)-total labelling of graphs was introduced by Havet and Yu. In this paper, we prove that, for planar graph G with maximum degree ∆ ≥ 12 and d = 2, the (2,1)-total labelling number λ2 (G) is at most ∆ + 2.

where E(v) is the set of edges that have v as an end-point. The total labelling λ of G is vertex-magic if every vertex has the same weight, and the graph G is vertexmagic if a vertex-magic total labelling of G exists. Magic labellings of graphs were introduced by Sedlácěk [5] in 1963, and vertex-magic total labellings first appeared in 2002 in [4]. For a dynamic survey of various forms of graph...

An -labelling of a graph is an assignment of nonnegative integers to the vertices of such that the difference between the labels assigned to any two adjacent vertices is at least zero and the difference between the labels assigned to any two vertices which are at distance two is at least one. The span of an   0,1 L G G   0,1 L -labelling is the maximum label number assigned to any vertex of...

Graph component labelling, which is a subset of the general graph colouring problem, is a computationally expensive operation that is of importance in many applications and simulations. A number of data-parallel algorithmic variations to the component labelling problem are possible and we explore their use with general purpose graphical processing units (GPGPUs) and with the CUDA GPU programmin...

An L(p, 1)-labelling of a graph is a function f from the vertex set to the positive integers such that |f(x) − f(y)| ≥ p if dist(x, y) = 1 and |f(x)− f(y)| ≥ 1 if dist(x, y) = 2, where dist(x, y) is the distance between the two vertices x and y in the graph. The span of an L(p, 1)labelling f is the difference between the largest and the smallest labels used by f plus 1. In 1992, Griggs and Yeh ...

A sum graph G is a graph with a mapping of the vertex set of G onto a set of positive integers S in such a way that two vertices of G are adjacent if and only if the sum of their labels is an element of S. In an exclusive sum graph the integers of S that are the sum of two other integers of S form a set of integers that label a collection of isolated vertices associated with the graph G. A grap...