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

We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals infect those belonging to the same community with higher probability than individuals in other communities. In community models the nodal infection probabili...

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...

In many applications of graph colouring the sizes of colour classes should not be too large. For example, in scheduling jobs (some of which could be performed at the same time), it is not good if the resulting schedule requires many jobs to occur at some specific time. An application of this type is discussed in [8]. A possible formalization of this restriction is the notion of equitable colour...

We study properties of binary codes with parameters close to the parameters of 1-perfect codes. An arbitrary binary (n = 2 − 3, 2n−m−1, 4) code C, i.e., a code with parameters of a triply-shortened extended Hamming code, is a cell of an equitable partition of the n-cube into six cells. An arbitrary binary (n = 2−4, 2, 3) codeD, i.e., a code with parameters of a triply-shortened Hamming code, is...

In many applications, not all the features used to represent data samples are important. Often only a few features are relevant for the prediction task. The choice of dependence measures often affect the final result of many feature selection methods. To select features that have complex nonlinear relationships with the response variable, the dependence measure should be equitable, a concept pr...