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《Discrete Mathematics》2022,345(3):112711
We investigate certain nonassociative binary operations that satisfy a four-parameter generalization of the associative law. From this we obtain variations of the ubiquitous Catalan numbers and connections to many interesting combinatorial objects such as binary trees, plane trees, lattice paths, and permutations. 相似文献
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Smarandachely邻点可区别全染色是指相邻点的色集合互不包含的邻点可区别全染色,是对邻点可区别全染色条件的进一步加强。本文研究了平面图的Smarandachely邻点可区别全染色,即根据2-连通外平面图的结构特点,利用分析法、数学归纳法,刻画了最大度为5的2-连通外平面图的Smarandachely邻点可区别全色数。证明了:如果$G$ 是一个$\Delta (G)=5$ 的2-连通外平面图,则$\chi_{\rm sat}(G)\leqslant 9$ 。 相似文献
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Toll convexity is a variation of the so-called interval convexity. A tolled walk between two non-adjacent vertices and in a graph is a walk, in which is adjacent only to the second vertex of and is adjacent only to the second-to-last vertex of . A toll interval between is a set . A set is toll convex, if for all . A toll closure of a set is the union of toll intervals between all pairs of vertices from . The size of a smallest set whose toll closure is the whole vertex set is called a toll number of a graph , . The first part of the paper reinvestigates the characterization of convex sets in the Cartesian product of two graphs. It is proved that the toll number of the Cartesian product of two graphs equals 2. In the second part, the toll number of the lexicographic product of two graphs is studied. It is shown that if is not isomorphic to a complete graph, . We give some necessary and sufficient conditions for . Moreover, if has at least two extreme vertices, a complete characterization is given. Furthermore, graphs with are characterized. Finally, the formula for is given — it is described in terms of the so-called toll-dominating triples or, if is complete, toll-dominating pairs. 相似文献
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This paper extends the framework for the valuation of life insurance policies and annuities by Andrés-Sánchez and González-Vila (2012, 2014) in two ways. First we allow various uncertain magnitudes to be estimated by means of fuzzy numbers. This applies not only to interest rates but also to the amounts to be paid out by the insurance company. Second, the use of symmetrical triangular fuzzy numbers allows us to obtain expressions for the pricing of life contingencies and their variability that are closely linked to standard financial and actuarial mathematics. Moreover, they are relatively straightforward to compute and understand from a standard actuarial point of view. 相似文献