A t-ruling set of a graph G = (V,E) is a vertex-subset S ⊆ V that is independent and satisfies the property that every vertex v ∈ V is at a distance of at most t from some vertex in S. A maximal independent set (MIS) is a 1-ruling set. The problem of computing an MIS on a network is a fundamental problem in distributed algorithms and the fastest algorithm for this problem is the O(logn)-round a...

This study introduces a new data set on personalism in ruling parties across the world’s democracies. We conceptualize party as extent to which are vehicles advance leaders’ personal political careers such that leader has more control over than do other senior elites and compare this concept with related ones. After describing measurement strategy demonstrating reliability validity, we show glo...

We define ruling invariants for even-valence Legendrian graphs in standard contact three-space. prove that rulings exist if and only the DGA of graph, introduced by first two authors, has an augmentation. set up usual polynomials various notions gradedness graph is four-valent, then ungraded polynomial appears Kauffman-Vogel's version Kauffman polynomial. Our are compatible with certain vertex-...

We study the formation of a ruling coalition in non-democratic societies where institutions do not enable political commitments. Each individual is endowed with a level of political power. The ruling coalition consists of a subset of the individuals in the society and decides the distribution of resources. A ruling coalition needs to contain enough powerful members to win against any alternativ...