A perfect coloring (equivalent concepts are equitable partition and design) of a graph $G$ is function $f$ from the set vertices onto some finite (of colors) such that every node color $i$ has exactly $S(i,j)$ neighbors $j$, where constants, forming matrix $S$ called quotient. If an adjacency simple $T$ on colors, then covering target by cover $G$. We characterize all coverings infinite square ...

end user satisfaction (eus) is one of the most widely used measures in assessing (efficiency/ effectiveness) of an information system. the goal of this research is to identify influential factors on (eus), based on justice theory. so we identified 8 influential factors on (eus) such as interactional justice, distributive justice, information system (is) performance expectation, equitable relate...

In this paper we introduce the common minimal equitable and vertex minimal equitable dominating graph and we get characterize the common minimal equitable and vertex minimal equitable dominating graph which are either connected or complete, some new results of these graphs are obtained. Mathematics Subject Classification: 05C70

Distributed simulation of large and complex networks requires equitable partitioning of the network model. We propose an iterative partitioning scheme for distributed network simulation that is based on a game theoretic model of simulated network nodes acting as players. We first model the cost function for the nodes and prove that a Nash equilibrium exists for the non-cooperative game in pure ...

For a finite, directed graph G = (V,E) we define the critical groupK(G) to be the cokernel of the transpose of the Laplacian matrix of G acting on Z , and K(G) to be its torsion subgroup. This generalizes the case of undirected graphs studied by Bacher, de la Harpe and Nagnibeda, and by Biggs. We prove a variety of results about these critical groups, among which are: that K(G/π) is a subgroup ...

We consider the discrete-time dynamics of a network of agents that exchange information according to a nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically. We present a fully decentralised algorithm that allows any agent to compute the final consensus value of the whole network in finite time using theminimumnumber of successive values of its own s...

In the forecasting of binary events, verification measures that are ‘‘equitable’’ were defined by Gandin and Murphy to satisfy two requirements: 1) they award all random forecasting systems, including those that always issue the same forecast, the same expected score (typically zero), and 2) they are expressible as the linear weighted sum of the elements of the contingency table, where the weig...

Because the partition coefficient is one of the most important parameters affecting microsegregation, the aim of this research is to experimentally analyse the partition coefficient in Al-Mg alloys. In order to experimentally measure the partition coefficient, a series of quenching experiments during solidification were carried out. For this purpose binary Al-Mg alloys containing 6.7 and 10.2 w...