A graph G is uniquely Kr-saturated if it contains no clique with r vertices and if for all edges e in the complement, G + e has a unique clique with r vertices. Previously, few examples of uniquely Kr-saturated graphs were known, and little was known about their properties. We search for these graphs by adapting orbital branching, a technique originally developed for symmetric integer linear pr...

A subset of vertices a graph is minimal if, within all subsets the same size, its vertex boundary minimal. We give complete, geometric characterization sets for planar integer lattice $X$. Our elucidates structure sets, and we are able to use it obtain several applications. show that neighborhood set characterize uniquely $X$: those which congruent any other size. also classify efficient have m...

Recently, Carlsson and Fuller [C. Carlsson, R. Fuller, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326] have introduced possibilistic mean, variance and covariance of fuzzy numbers and Fuller and Majlender [R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003) 363–374] have in...

This paper is a brief summary of “M.Takahashi, T.Murofushi, S.Asahina, A new necessary and sufficient condition for the Egoroff theorem in non-additive measure theory, Fuzzy Sets and Systems, to appear.” This paper states that a newly defined condition, called condition (M), is a necessary and sufficient condition for the Egoroff theorem in non-additive measure theory. The existing necessary an...