Twin-width and generalized coloring numbers

Width invariant approximation of fuzzy numbers

In this paper, we consider the width invariant trapezoidal and triangularapproximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserv...

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.

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...

Zero forcing, tree width, and graph coloring

We show that certain types of zero-forcing sets for a graph give rise to chordal supergraphs and hence to proper colorings. Zero-forcing was originally defined to provide a bound for matrix minimum rank problems [1], but is interesting as a graph-theoretic notion in its own right [5], and has applications to mathematical physics, such as quantum systems [3]. There are different flavors of zero-...

Addition two generalized fuzzy numbers