The frequency assignment problem has been started from the discovery that transmitters, received the same or closely related frequencies, had interferences with one another. Nearly three decade back this problem has been modelled as a graph labelling problem. This labelling has several variations depending upon the type of assignment of frequency to transmitters. Here we shall discuss about som...

Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs of the graph grammars by probabilities. Stochastic properties of these graphs are expressed using PCTL, a probabilistic extension of computation tree logic. ...

A graph G is a difference graph iff there exists S ⊂ IN such that G is isomorphic to the graph DG(S) = (V,E), where V = S and E = {{i, j} : i, j ∈ V ∧ |i− j| ∈ V }. It is known that trees, cycles, complete graphs, the complete bipartite graphs Kn,n and Kn,n−1, pyramids and n-sided prisms (n ≥ 4) are difference graphs (cf. [4]). Giving a special labelling algorithm, we prove that cacti with a gi...

Given any fixed nonnegative integer values h and k, the L(h, k)-labelling problem consists in an assignment of nonnegative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest ass...

Let G be a finite graph with p vertices and q edges. A vertex magic total labelling is a bijection from the union of the vertex set and the edge set to the consecutive integers 1, 2, 3, . . . , p + q with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k for some constant k. Such a labelling is E-super, if the lab...

Graph theory and its applications attract several researchers from different areas of research. It is used to model wide range systems, for example in biological system studying chaotic systems. Decomposition complex graphs into simple small very helpful study that A complete classification given circulant degree 5 allow an Orthogonal Double Cover by some graphs. Whenever such a cover exists, o...

In this work we consider a generalization of graph flows. A flow is, in its simplest formulation, labelling the directed edges with real numbers subject to various constraints. common constraint is conservation vertex, meaning that sum labels on incoming vertex equals those outgoing edges. One easy fact if conserving all but one then it also remaining one. our do not label numbers, elements fro...