Abstract: Vertex configuration for a vertex in an orthogonal
pseudo-polyhedron is an identity of a vertex that is determined by the
number of edges, dihedral angles, and non-manifold properties
meeting at the vertex. There are up to sixteen vertex configurations
for any orthogonal pseudo-polyhedron (OPP). Understanding the
relationship between these vertex configurations will give us insight
into the structure of an OPP and help us design better algorithms for
many 3-dimensional geometric problems. In this paper, 16 vertex
configurations for OPP are described first. This is followed by a
number of formulas giving insight into the relationship between
different vertex configurations in an OPP. These formulas
will be useful as an extension of orthogonal polyhedra usefulness on
pattern analysis in 3D-digital images.
Abstract: The unique structural configuration found in human foot allows easy walking. Similar movement is hard to imitate even for an ape. It is obvious that human ambulation relates to the foot structure itself. Suppose the bones are represented as vertices and the joints as edges. This leads to the development of a special graph that represents human foot. On a footprint there are point-ofcontacts which have contact with the ground. It involves specific vertices. Theoretically, for an ideal ambulation, these points provide reactions onto the ground or the static equilibrium forces. They are arranged in sequence in form of a path. The ambulating footprint follows this path. Having the human foot graph and the path crossbred, it results in a representation that describes the profile of an ideal ambulation. This profile cites the locations where the point-of-contact experience normal reaction forces. It highlights the significant of these points.
Abstract: The similarity comparison of RNA secondary
structures is important in studying the functions of RNAs. In recent
years, most existing tools represent the secondary structures by
tree-based presentation and calculate the similarity by tree alignment
distance. Different to previous approaches, we propose a new method
based on maximum clique detection algorithm to extract the maximum
common structural elements in compared RNA secondary structures.
A new graph-based similarity measurement and maximum common
subgraph detection procedures for comparing purely RNA secondary
structures is introduced. Given two RNA secondary structures, the
proposed algorithm consists of a process to determine the score of the
structural similarity, followed by comparing vertices labelling, the
labelled edges and the exact degree of each vertex. The proposed
algorithm also consists of a process to extract the common structural
elements between compared secondary structures based on a proposed
maximum clique detection of the problem. This graph-based model
also can work with NC-IUB code to perform the pattern-based
searching. Therefore, it can be used to identify functional RNA motifs
from database or to extract common substructures between complex
RNA secondary structures. We have proved the performance of this
proposed algorithm by experimental results. It provides a new idea of
comparing RNA secondary structures. This tool is helpful to those
who are interested in structural bioinformatics.
Abstract: Graph decompositions are vital in the study of
combinatorial design theory. A decomposition of a graph G is a
partition of its edge set. An n-sun graph is a cycle Cn with an edge
terminating in a vertex of degree one attached to each vertex. In this
paper, we define n-sun decomposition of some even order graphs
with a perfect matching. We have proved that the complete graph
K2n, complete bipartite graph K2n, 2n and the Harary graph H4, 2n have
n-sun decompositions. A labeling scheme is used to construct the n-suns.
Abstract: Graph decompositions are vital in the study of combinatorial design theory. Given two graphs G and H, an H-decomposition of G is a partition of the edge set of G into disjoint isomorphic copies of H. An n-sun is a cycle Cn with an edge terminating in a vertex of degree one attached to each vertex. In this paper we have proved that the complete graph of order 2n, K2n can be decomposed into n-2 n-suns, a Hamilton cycle and a perfect matching, when n is even and for odd case, the decomposition is n-1 n-suns and a perfect matching. For an odd order complete graph K2n+1, delete the star subgraph K1, 2n and the resultant graph K2n is decomposed as in the case of even order. The method of building n-suns uses Walecki's construction for the Hamilton decomposition of complete graphs. A spanning tree decomposition of even order complete graphs is also discussed using the labeling scheme of n-sun decomposition. A complete bipartite graph Kn, n can be decomposed into n/2 n-suns when n/2 is even. When n/2 is odd, Kn, n can be decomposed into (n-2)/2 n-suns and a Hamilton cycle.