On Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers

On generalized fuzzy numbers

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

Stirling Numbers and Generalized Zagreb Indices

We show how generalized Zagreb indices $M_1^k(G)$ can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.

Addition two generalized fuzzy numbers

On Generalized Schur Numbers

Let L(t) represent the equation x1 + x2 + · · · + xt−1 = xt. For k > 1, 0 6 i 6 k − 1, and ti > 3, the generalized Schur number S(k; t0, t1, . . . , tk−1) is the least positive integer m such that for every k-colouring of {1, 2, . . . ,m}, there exists an i ∈ {0, 1, . . . , k − 1} such that there exists a solution to L(ti) that is monochromatic in colour i. In this paper, we report twenty-six p...

On generalized Ramsey numbers

Let f1 and f2 be graph parameters. The Ramsey number r(f1 ≥ m; f2 ≥ n) is defined as the minimum integer N such that any graph G on N vertices, either f1(G) ≥ m or f2(G) ≥ n. A general existence condition is given and a general upper bound is shown in this paper. In addition, suppose the number of triangles in G is denoted by t(G). We verify that (1− o(1))(24n) ≤ r(t ≥ n; t ≥ n) ≤ (1 + o(1))(48...