Search Results

In this note we continue the work of Chon, as well as Mezzomo, Bedregal, and Santiago, by studying algebraic operations on fuzzy posets and bounded fuzzy lattices. We first prove that fuzzy posets are closed under finite direct products whenever ...

The super edge-connectivity of a connected graph G, denoted by ${\lambda }^{\prime }\left(G\right)$, if exists, is the minimum number of edges whose deletion disconnects the graph such that each component has no isolated vertices. The direct product of graphs G and H, denoted by $\mathrm{...}$$\left(,,\right)\left(\right)\left(\right)$$\left({}_{\mathrm{}},,{}_{\mathrm{}}\right)$$\left({}_{\mathrm{}},,{}_{\mathrm{}}\right)$$$${}_{\mathrm{}}{}_{\mathrm{}}\left(\right)$${}_{\mathrm{}}{}_{\mathrm{}}\left(\right)$${}^{}\left(,,{}_{}\right)\mathrm{}{}^{}\left(\right)\mathrm{}\underset{\left(\right)}{}\left({}_{},\left(\right),,{}_{},\left(\right)\right)\mathrm{}$$\left|\right|$$\mathrm{}\left(\right)\mathrm{}$${}_{}$$\left|\right|$$\mathrm{}\left(\right)\mathrm{}$${}_{}$

Hedetniemi's conjecture, a significant problem in graph theory, was disproved by Shitov in 2019. This breakthrough stimulates us to consider the signed graphs version of Hedetniemi's conjecture, where signed graphs are graphs with an assignment ...

In this note we exhibit various ways of obtaining a wide range of soluble partially ordered sets. These are the posets on which every transitive system can be completed. In particular, algebraic operations such as the sums and products of posets ...

Let A be an MV-algebra. An $(\odot ,\vee )$-derivation on A is a map $d:A\to A$ satisfying: $d(x\odot y)=(d(x)\odot y)\vee (x\odot d(y))$ for  all $x,y\in A$. This paper initiates the study of $(\odot ,\vee )$-derivations on MV-algebras. Several families of $(\odot ,\vee )$-derivations on an MV-algebra are ...$$$$

One can construct t-norms on product posets by direct products of t-norms straightforwardly. However, there exist many t-norms on product posets which are not direct products. In this paper, some new t-norms which are not direct products on ...

Let G , H be graphs and G ⁎ H represent a particular graph product of G and H. We define im ( G ) to be the largest t such that G has a K t-immersion and ask: given im ( G ) = t and im ( H ) = r, how large is im ( G ⁎ H )? Best ...

A k-total coloring of a graph G is an assignment of k colors to its elements (vertices and edges) so that adjacent or incident elements have different colors. The total chromatic number is the smallest integer k for which the graph G has a k-...

If each minimal dominating set in a graph is a minimum dominating set, then the graph is called well-dominated. Since the seminal paper on well-dominated graphs appeared in 1988, the structure of well-dominated graphs from several ...

Given a graph $G=(V(G),E(G))$, a mapping from V(G) to $\{1,\dots ,|V(G)|\}$ (the numbers $1,\dots ,|V(G)|$ are usually called colors) is said to be a 2-distance coloring of G if any two vertices at distance at most two from each other receive different colors. Such ...${}_{\mathrm{}}$

In [16] Nowakowski and Rall listed a series of conjectures involving several different graph products. In particular, they conjectured that $i(G\times H)\ge i(G)i(H)$ where i(G) is the independent domination number of G and $G\times H$ is the direct product of ...$$${}_{}$

The bond between L-fuzzy formal contexts can be defined as a (Galois) connection between L-fuzzy concept lattices of L-fuzzy formal contexts. The selection of appropriate bond from the set of all bonds between L-fuzzy formal contexts ...

Let H ≤ S n be an intransitive group with orbits Ω 1 , Ω 2 , … , Ω k. Then certainly H is a subdirect product of the direct product of its projections onto each orbit, H | Ω 1 × H | Ω 2 × … × H | Ω k. Here we provide a polynomial time ...

A fractional matching of a graph G is a function f giving each edge a number in [0, 1] so that ${\sum }_{e\in {\mathrm{\Gamma }}_G(v)}f(e)\le 1$ for each $v\in V(G)$, where ${\mathrm{\Gamma }}_G(v)$ is the set of edges incident to v in G. The fractional matching number of G, denoted by ${\mu }_f(G)$, is the ...${}_{}$${}_{}{}_{}$

A graph is well-dominated if all of its minimal dominating sets have the same cardinality. It is proved that there are exactly eleven connected, well-dominated, triangle-free graphs whose domination number is at most 3. We prove that at least one ...${}_{\mathrm{}}$${}_{\mathrm{}}$

Based on results concerning equivalences on direct products of sets, a representation of aggregation functions acting on products of ordered structures by means of aggregation functions acting component-wise is obtained and discussed. ...

Let G be a graph with an even number of vertices. The matching preclusion number of G, denoted by m p ( G ), is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching. G is maximally matched if ...

The direct product encoding of a string a∈ { 0,1}ⁿ on an underlying domain V⊆ (k^[n]) is a function DP_V(a) that gets as input a set S∈ V and outputs a restricted to S. In the direct product testing problem, we are given a function F:V→ { 0,1}^k, and our ...

Let G be a graph. It is known that Aut( G ) × Z 2 is contained in Aut( G × K 2 ) where G × K 2 is the direct product of G with K 2. When this inclusion is strict, the graph G is called unstable. We define the index of instability of G ...

The tensor product ( G 1 , G 2 , G 3 ) of graphs G 1, G 2 and G 3 is defined by V ( G 1 , G 2 , G 3 ) = V ( G 1 ) × V ( G 2 ) × V ( G 3 ) and ...