A pure simplicial complex of dimension d − 1 (or a (d − 1)-complex, for short) is any family C of d-element subsets of a set V (tipycally, V = [n] := {1, . . . , n}). Elements of C are called facets of C and any subset of a facet is called a face. More precisely, a k-face is a face with k + 1 elements. Faces of dimensions 0, 1, and d − 2 are called, respectively, vertices, edges and ridges of C...

In this paper, a general way to determine the adjacency graph of linear feedback shift registers (LFSRs) with characteristic polynomial (1 + x)c(x) from the adjacency graph of LFSR with characteristic polynomial c(x) is discussed, where c(x) can be any polynomial. As an application, the adjacency graph of LFSRs with characteristic polynomial (1+ x)p(x) are determined, where p(x) is a primitive ...

The metric dimension is quite a well-studied graph parameter. Recently, the adjacency metric dimension and the local metric dimension have been introduced. We combine these variants and introduce the local adjacency metric dimension. We show that the (local) metric dimension of the corona product of a graph of order n and some non-trivial graph H equals n times the (local) adjacency metric dime...

Adjacencies stand at the beginning of a multitude of planning tasks. Especially in hospital planning they are essential for describing relationships between different organizational units – e.g. ‘close’, ‘distant’ or ‘neutral’. Mathematically, these terms map to relative weights between each pair of units in the range [-1, 1] which are put into a (symmetric) adjacency matrix. This matrix subseq...