Let $G$ be a simple connected graph. In this paper, Szeged dimension and PI$_v$ dimension of graph $G$ are introduced. It is proved that if $G$ is a graph of Szeged dimension $1$ then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Sze...

Motion capture devices have been utilized in producing several contents, such as movies and video games. However, since motion capture devices are expensive and inconvenient to use, motions segmented from captured data was recycled and synthesized to utilize it in another contents, but the motions were generally segmented by contents producers in manual. Therefore, automatic motion segmentation...

We study the maximum induced matching problem on a graph G. Induced matchings correspond to independent sets in L2(G), the square of the line graph of G. The problem is NP-complete on bipartite graphs. In this work, we show that for a number of graph families with forbidden vertex orderings, almost all forbidden patterns on three vertices are preserved when taking the square of the line graph. ...

For given graphs G and H , let |Hom(G,H)| denote the set of graph homomorphisms from G to H . We show that for any finite, n-regular, bipartite graph G and any finite graph H (perhaps with loops), |Hom(G,H)| is maximum when G is a disjoint union of Kn,n’s. This generalizes a result of J. Kahn on the number of independent sets in a regular bipartite graph. We also give the asymptotics of the log...

In this paper1 we study the on-line version of maximum-weighted hereditary subgraph problems. In our on-line model, the final instance (a graph with n vertices) is revealed in t clusters, n t ≤ ≤ 2 . We first focus on an on-line version of the maximumweighted hereditary subgraph problem. Then, we deal with the particular case of the independent set problem. We are interested in two types of res...

Given a totally positive matrix, can one insert line (row or column) between two given lines while maintaining total positivity? This question was first posed and solved by Johnson Smith who gave an algorithm that results in possible insertion. In this work, we revisit problem. First, show every matrix be associated with certain vertex-weighted graph such way the entries of are equal to sums ov...

This paper presents a multi-objective Particle Swarm Optimization (PSO) algorithm for worker assignment and mixed-model assembly line balancing problem when task times depend on the worker’s skill level. The objectives of this model are minimization of the number of stations (equivalent to the maximization of the weighted line efficiency), minimization of the weighted smoothness index and minim...

A minimum spanning tree of a weighted graph is a tree of the graph which contains all the vertices of the graph and the sum of weights of all its edges are minimum among all such possible trees of the graph. In this paper, we have proposed a new technique and its corresponding algorithm to construct the minimum spanning tree of a weighted graph. This new algorithm is based on the weight matrix ...