Optical motion capture (MOCAP) is a commonly used technology to record the of non-rigid objects with high accuracy in 3D space. However, MOCAP data has be processed further before it can used. The scattered reconstructed must constitute human configuration by labelling process according predefined template, and missing markers have produce stable trajectory. In this work, we propose novel metho...

We establish new lower and upper bounds for the real number graph labelling problem. As an application, we completely determine the optimum spans of L(p, q)-labellings of the infinite triangular plane lattice (solving an open problem of Griggs).

Finite, undirected graphs without self-loops are considered in the paper. The goal is to nd a protocol for local computation which, starting with a uniform labelling of graph nodes, eventually terminates with a labelling being an enumeration of nodes. It is known from 4] that for some (\ambiguous") graphs of the considered family such a protocol does not exist; in the present paper a protocol i...

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.

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...

A k-L(2, 1)-labelling of a graph G is a mapping f : V (G) → {0, 1, 2, . . . , k} such that |f(u)− f(v)| ≥ 2 if uv ∈ E(G) and f(u) 6= f(v) if u, v are distance two apart. The smallest positive integer k such that G admits a k-L(2, 1)-labelling is called the λ-number of G. In this paper we study this quantity for cubic Cayley graphs (other than the prism graphs) on dihedral groups, which are call...

Line labelling has been used to determine whether a two-dimensional (2D) line drawing object is a possible or impossible representation of a three-dimensional (3D) solid object. However, the results are not sufficiently robust because the existing line labelling methods do not have any validation method to verify their own result. In this research paper, the concept of graph colouring is applie...

Labelling problems for graphs consist in building distributed data structures, making it possible to check a given graph property or to compute a given function, the arguments of which are vertices. For an inductively computable function D, if G is a graph with n vertices and of clique-width at most k, where k is fixed, we can associate with each vertex x of G a piece of information (bit sequen...

The results presented in this paper are parts of my doctoral thesis [ 193; the algorithm and some of the characterizations in Section 7 have been introduced in [ 181. Motivation for isometric embeddings into Hamming graphs has come from communication theory (Graham and Pollak [ 121) an-d linguistics (Firsov 1181). Isometric subgraphs of Hamming graphs also appear in biology as “quasi-species” (...

We begin the study of distinguishing geometric graphs. Let G be a geometric graph. An automorphism of the underlying graph that preserves both crossings and noncrossings is called a geometric automorphism. A labelling, f : V (G) → {1, 2, . . . , r}, is said to be rdistinguishing if no nontrivial geometric automorphism preserves the labels. The distinguishing number of G is the minimum r such th...