A proper coloring of a graph is a partition of its vertex set into stable sets, where each part corresponds to a color. For a vertex-weighted graph, the weight of a color is the maximum weight of its vertices. The weight of a coloring is the sum of the weights of its colors. Guan and Zhu defined the weighted chromatic number of a vertex-weighted graph G as the smallest weight of a proper colori...

Due to exponential growth of complex data, graph structure has become increasingly important to model various entities and their interactions, with many interesting applications including, bioinformatics, social network analysis, etc. Depending on the complexity of the data, the underlying graph model can be a simple directed/undirected and/or weighted/un-weighted graph to a complex graph (aka ...

This paper presents a multi-objective simulated annealing algorithm for the mixed-model assembly line balancing with stochastic processing times. Since, the stochastic task times may have effects on the bottlenecks of a system, maximizing the weighted line efficiency (equivalent to the minimizing the number of station), minimizing the weighted smoothness index and maximizing the system reliabil...

Usually the boundary of a community in a network is drawn between nodes and thus crosses its outgoing links. If we construct overlapping communities by applying the link-clustering approach nodes and links interchange their roles. Therefore, boundaries must drawn through the nodes shared by two or more communities. For the purpose of community evaluation we define a conductance of boundary node...