It is known that the Alexander polynomial detects fibered knots and 3-manifolds that fiber over the circle. In this note, we show that when the Alexander polynomial becomes inconclusive, the notion of knot adjacency can be used to obtain obstructions to fibering of knots and of 3-manifolds. As an application, given a fibered knot K′, we construct infinitely many non-fibered knots that share the...

We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, i.e. graphs on N vertices where every edge is chosen independently and with probability p ≡ p(N). We rescale the matrix so that its bulk eigenvalues are of order one. Under the assumption pN N, we prove the universality of eigenvalue distributions both in the bulk and at the edge of the spectrum. More precisely, we pro...

Let G be a simple graph with adjacency matrix A (= AG). The eigenvalues and the spectrum of A are also called the eigenvalues and the spectrum of G, respectively. If we consider a matrix Q = D + A instead of A, where D is the diagonal matrix of vertex–degrees (in G), we get the signless Laplacian eigenvalues and the signless Laplacian spectrum, respectively. For short, the signless Laplacian ei...

In a certain class of point-line geometries, called locally projective near polygons, which includes dual polar spaces and generalised 2n-gons, surjective adjacency preserving mappings are already collineations.

The spectrum of a graph has been widely used in graph theory to characterise the properties of a graph and extract information from its structure. It has been less popular as a representation for pattern matching for two reasons. Firstly, more than one graph may share the same spectrum. It is well known, for example, that very few trees can be uniquely specified by their spectrum. Secondly, the...

The accurate selection of a processing plant site can result in decreasing total mining cost. This problem can be solved by multi-criteria decision-making (MCDM) methods. This research introduces a new approach by integrating fuzzy AHP and gray MCDM methods to solve all decision-making problems. The approach is applied in the case of a copper mine area. The critical criteria are considered adja...

In this paper, we discuss the adjacency structures of some classes of 0-1 polytopes including knapsack polytopes, set covering polytopes and 0-1 polytopes represented by complete sets of implicants. We show that for each class of 0-1 polytope, non-adjacency test problems are NP-complete. For equality constrained knapsack polytopes, we can solve adjacency test problems in pseudo polynomial time.

The Harary-Sachs theorem for k-uniform hypergraphs equates the codegree-d coefficient of adjacency characteristic polynomial a uniform hypergraph with weighted sum subgraph counts over certain multi-hypergraphs d edges. We begin by showing that classical graphs is indeed special case this general theorem. To end we apply generalized to leading coefficients various hypergraphs. In particular, pr...

Pedigree polytopes are extensions of the classical Symmetric Traveling Salesman Problem polytopes whose graphs (1-skeletons) contain the TSP polytope graphs as spanning subgraphs. While deciding adjacency of vertices in TSP polytopes is coNP-complete, Arthanari has given a combinatorial (polynomially decidable) characterization of adjacency in Pedigree polytopes. Based on this characterization,...

Pseudo noun incorporation constructions in Sakha and Tamil obey a strict linear adjacency condition, such that not only the NP but its head noun must be adjacent to the verb at PF. I argue that this adjacency condition can be explained if the head of the NP adjoins to the verb to create a unit that is interpreted as a complex predicate at LF. The resulting structure can be linearized at PF if a...