We describe the structure of the unique minimal test set T for a family of vertex cover problems. The set T corresponds to the Gröbner basis of the binomial ideal for the problem as described in [1]. While T has a surprisingly simple structure, in particular when the underlying graph is complete, it is NP -complete to decide whether the test set contains an improving element for a given feasibl...

Let $$L_n$$ be a line graph with n edges and $${{\mathcal {F}}}(L_n)$$ the facet ideal of its matching complex. In this paper, we provide irreducible decomposition some exact formulas for projective dimension regularity .

An important predictor of historical sound change, functional load, fails to capture insights from speech perception. Building on ideal observer models of word recognition, we devise a new definition of functional load that incorporates both a priori expectedness and perceptual information. We explore this new measure with a simple model and find that it outperforms tra-

Recently, Katre et al. introduced the concept of coprime index a graph. They asked to characterize graphs for which is same as clique number. In this paper, we partially solve problem. fact, prove that number and zero-divisor graph an ordered set ring Zpn coincide. Also, it proved annihilating ideal graphs, co-annihilating comaximal commutative rings can be realized specially constructed posets...

Let R be a commutative finite principal ideal ring with unity, and letG(R) be the simple graph consisting of nontrivial proper ideals of R as vertices such that two vertices I and J are adjacent if they have nonzero intersection. In this paper we continue the work done by Abu Osba. We calculate the radius, eccentricity, domination number, independence number, geodetic number, and the hull numbe...

The study of graph vertex colorability from an algebraic perspective has introduced novel techniques and algorithms into the field. For instance, k-colorability of a graph can be characterized in terms of whether its graph polynomial is contained in a certain ideal. In this paper, we interpret unique colorability in an analogous manner and prove an algebraic characterization for uniquely k-colo...

This paper explores finding existence of undirected hamiltonian paths in a graph using lumped/ideal circuits, specifically low-pass filters. While other alternatives are possible, a first-order RC low-pass filter is chosen to describe the process. The paper proposes a way of obtaining time complexity for counting the number of hamiltonian paths in a graph, and then shows that the time complexit...

Abstract Let R be a commutative ring with identity. Let G be a graph with vertices as elements of R, where two distinct vertices a and b are adjacent if and only if there is a maximal ideal of R containing both. In this paper we show that a ring R is finite if and only if clique number of the graph G (associated with R as above) is finite. We also have shown that for a semilocal ring R, the chr...

A polynomial ideal encoding topplings in the abelian sandpile model on a graph is introduced. A Grr obner basis of this ideal is interpreted combinatorially in terms of well-connected subgraphs. This gives rise to algorithms to determine the identity and the operation in the group of recurrent conngurations. Tas de sable, id eaux polynomiaux et leurs bases de Grr obner R esum e : Nous introduis...