We propose a weighted common subgraph (WCS) matching algorithm to find the most similar subgraphs in two labeled weighted graphs. WCS matching, as a natural generalization of the equal-sized graph matching or subgraph matching, finds wide applications in many computer vision and machine learning tasks. In this paper, the WCS matching is first formulated as a combinatorial optimization problem o...

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...

Given a Cartesian product G = GI x x G,, (m > 2) of nontrivial connected graphs G, and the base d, dimension D de Bruijn graph B(d,D), it is investigated under which conditions G is (or is not) a subgraph of B(d, D). We present a complete solution of this problem for the case D 3 4. For D = 3, we give partial results including a complete solution for the case that G is a torus, i.e., G is the C...

This paper introduces the subgraph nomination inference task, in which example subgraphs of interest are used to query a network for similarly interesting subgraphs. type problem appears time and again real world problems connected to, example, user recommendation systems structural retrieval tasks social biological/connectomic networks. We formally define framework with an emphasis on notion u...

Images of fuzzy relations provide powerful access to fuzzifications of properties of and/or relationships between fuzzy sets. As an important example, images of fuzzy orderings canonically lead to a concept of ordering of fuzzy sets. This contribution studies in which way the partial (i.e. componentwise) monotonicity of an n-ary mapping transfers to its extension to fuzzy sets.

Graph theory has many real-world applications and is rich in theoretical results, especially for studying interconnection among elements in natural and man-made systems. In recent studies of complex control system, directed graph was introduced to define and interpret the interconnection structure underlying the dynamics of the interacting subsystems. Similarly, Fuzzy State Space Model (FSSM) w...

We investigate the structure of isometric subgraphs of hypercubes (i.e., partial cubes) which do not contain finite convex subgraphs contractible to the 3-cube minus one vertex Q3 (here contraction means contracting the edges corresponding to the same coordinate of the hypercube). Extending similar results for median and cellular graphs, we show that the convex hull of an isometric cycle of suc...

let $r$ be a commutative ring with identity and $mathbb{a}(r)$ be the set   of ideals of $r$ with non-zero annihilators. in this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $r$, denoted by $mathbb{ag}_p(r)$. it is a (undirected) graph with vertices $mathbb{a}_p(r)=mathbb{a}(r)cap mathbb{p}(r)setminus {(0)}$, where   $mathbb{p}(r)$ is...