Steiner Distance in Product Networks

For a connected graph $G$ of order at least $2$ and $S\subseteq V(G)$, the \emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. Let $n$ and $k$ be two integers with $2\leq k\leq n$. Then the \emph{Steiner $k$-eccentricity $e_k(v)$} of a vertex $v$ of $G$ is defined by $e_k(v)=\max \{d_G(S)\,|\,S\subseteq V(G), \ |S|=k, \ and \ v\in S\}$. Furthermore, the \emph{Steiner $k$-diameter} of $G$ is $sdiam_k(G)=\max \{e_k(v)\,|\, v\in V(G)\}$. In this paper, we investigate the Steiner distance and Steiner $k$-diameter of Cartesian and lexicographical product graphs. Also, we study the Steiner $k$-diameter of some networks.Comment: 29 pages, 4 figure

The Deviant Behavior in Kevin Kwan’s Rich People Problems

From the research results 18 data were found which indicate an aberration of behavior and classified into normative and differential association process performed by Eddie cheng was performed to obtain the property of his grandmother to make himself rich and equal to his other relatives. Different family backgrounds create conflicting norms that make Eddie commit deviant behavior. Therefore Eddie's perversion was intended to remain in the environment, though not consistent with its background to obtain and inherit

Matching Preclusion and Conditional Matching Preclusion Problems for Twisted Cubes

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. In this paper, we find the matching preclusion number and the conditional matching preclusion number for twisted cubes, an improved version of the well-known hypercube. Moreover, we also classify all the optimal matching preclusion sets

Conditional Strong Matching Preclusion of the Alternating Group Graph

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. Park and Ihm introduced the problem of strong matching preclusion under the condition that no isolated vertex is created as a result of faults. In this paper, we find the conditional strong matching preclusion number for the $n$-dimensional alternating group graph $AG_n$

The Conditional Strong Matching Preclusion of Augmented Cubes

The strong matching preclusion is a measure for the robustness of interconnection networks in the presence of node and/or link failures. However, in the case of random link and/or node failures, it is unlikely to find all the faults incident and/or adjacent to the same vertex. This motivates Park et al. to introduce the conditional strong matching preclusion of a graph. In this paper we consider the conditional strong matching preclusion problem of the augmented cube $AQ_n$, which is a variation of the hypercube $Q_n$ that possesses favorable properties

Fine-grained traffic state estimation and visualisation

Tools for visualising the current traffic state are used by local authorities for strategic monitoring of the traffic network and by everyday users for planning their journey. Popular visualisations include those provided by Google Maps and by Inrix. Both employ a traffic lights colour-coding system, where roads on a map are coloured green if traffic is flowing normally and red or black if there is congestion. New sensor technology, especially from wireless sources, is allowing resolution down to lane level. A case study is reported in which a traffic micro-simulation test bed is used to generate high-resolution estimates. An interactive visualisation of the fine-grained traffic state is presented. The visualisation is demonstrated using Google Earth and affords the user a detailed three-dimensional view of the traffic state down to lane level in real time

The Market Fraction Hypothesis under different GP algorithms

In a previous work, inspired by observations made in many agent-based financial models, we formulated and presented the Market Fraction Hypothesis, which basically predicts a short duration for any dominant type of agents, but then a uniform distribution over all types in the long run. We then proposed a two-step approach, a rule-inference step and a rule-clustering step, to testing this hypothesis. We employed genetic programming as the rule inference engine, and applied self-organizing maps to cluster the inferred rules. We then ran tests for 10 international markets and provided a general examination of the plausibility of the hypothesis. However, because of the fact that the tests took place under a GP system, it could be argued that these results are dependent on the nature of the GP algorithm. This chapter thus serves as an extension to our previous work. We test the Market Fraction Hypothesis under two new different GP algorithms, in order to prove that the previous results are rigorous and are not sensitive to the choice of GP. We thus test again the hypothesis under the same 10 empirical datasets that were used in our previous experiments. Our work shows that certain parts of the hypothesis are indeed sensitive on the algorithm. Nevertheless, this sensitivity does not apply to all aspects of our tests. This therefore allows us to conclude that our previously derived results are rigorous and can thus be generalized