It is well known that, in general, part of the spectrum of a graph can be obtained from the adjacency matrix of its quotient graph given by a regular partition. In this paper, a method that gives all the spectrum, and also ...

Let $\Gamma$ be a regular (connected) graph with $n$ vertices and $d+1$ distinct eigenvalues. As a main result, it is shown that $\Gamma$ is an $r$-antipodal distance-regular graph if and only if the distance graph $\Gamma_d$ ...

A graph $\G$ with diameter $D$ and $d+1$ distinct eigenvalues is said to be {\it $(\ell,m)$-walk-regular}, for some integers $\ell\in[0,d]$ and $m\in[0,D]$, $\ell\ge m$, if the number of walks of length $i\in [0,\ell]$ ...

Given a simple connected graph $\Gamma$ and a subset of its vertices $C$, the pseudo-distance-regularity around $C$ generalizes, for not necessarily regular graphs, the notion of completely regular code. Up to now, most ...

We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. Let G be a graph with vertex set V , diameter D, adjacency matrix A, and ...

The spectrum of a graph usually provides a lot of information about its combinatorial structure. Moreover,from the spectrum, the so-called predistance polynomials can be defined, as a generalization, for any graph, of the ...

A -graph is a -regular graph with girth and a -cage is a -graph with the fewest possible number of vertices . Constructing -cages and determining the order are both very hard problems. For this reason, an intensive line ...

Many destinations are implementing various water management alternatives to diminish the environmental impacts of tourism and increase sustainability. These efforts toward sustainability can be understood as part of corporate ...

The main result of this paper is the introduction of marked graphs and the marked graph polynomials ( -polynomial) associated with them. These polynomials can be defined via a deletion-contraction operation. These polynomials ...

Matroids arise from the abstract notion of dependency. Matroids can be studied from different points of view. From linear algebra we know matrices, which can be seen as matroids, however matroids generalise the concept of ...