For a given graph G of order n, an L(2, 1)-labelling is defined as a function f : V (G) → {0, 1, 2, · · ·} such that |f(u)− f(v)| ≥ 2 when dG(u, v) = 1 and |f(u)− f(v)| ≥ 1 when dG(u, v) = 2, is the minimum length of a path between u and v. A k−L(2, 1)-labelling is an L(2, 1)-labelling such that no label is greater than k. The L(2, 1)-labelling number of G, denoted by λ(G), is the smallest numb...

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...

An (2,1) L -labelling of a graph ( , ) G V E = is 2,1( ) G λ a function f from the vertex set ( ) V G to the set of non-negative integers such that adjacent vertices get numbers at least two apart, and vertices at distance two get distinct numbers. The (2,1) L -labelling number denoted by 2,1( ) G λ of G is the minimum range of labels over all such labelling. In this article, it is shown that, ...

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

An event structures is a mathematical model of a concurrent process. It consists of a set of local events ordered by a causality relation and separated by a conflict relation. A global state, or configuration, is an order ideal whose elements are pairwise not in conflict. Configurations, ordered by subset inclusion, form a poset whose Hasse diagram codes the state-transition graph of the proces...

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...

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...

Let G =( V, E) be a graph. A bijectionf: V+{ 1,2,. ., 1 VI} IS called a prime labelling if for each e = {u, u} in E, we have GCD(f(u),f(u))= 1. A graph admits a prime labelling is called a prime graph. Around ten years ago, Roger Entringer conjectured that every tree is prime. So far, this conjecture is still unsolved. In this paper, we show that the conjecture is true for trees of order up to ...

In this paper, we tackle the problem of matching of objects in video in the context of the rough indexing paradigm. The approach developed is based on matching of region adjacency graphs (RAG) of pre-segmented objects. In the context of the rough indexing paradigm, the video data are of very low resolution and segmentation is consequently inaccurate. Hence the RAGs vary with the time. The contr...