We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph Fk(G) of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent ...

We describe, in a very explicit way, a method for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not)

A (1, = `)-identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ` have distinct closed in-neighbourhoods within C. In this paper, we give some ...

We study the (delta;D) and (delta;N) problems for double-step digraphs considering the unilateral distance, which is the minimum between the distance in the digraph and the distance in its converse digraph, the latter ...

The (¿;D) (degree/diameter) problem consists of nding the largest possible number of vertices n among all the graphs with maximum degree ¿ and diameter D. We consider the (¿;D) problem for maximal planar bipartite graphs, ...

We present a new kind of digraphs, called cyclic Kautz digraphs CK(d, `), which are subdigraphs of the well-known Kautz digraphs K(d, `). The latter have the smallest diameter among all digraphs with their number of vertices ...

A generalization of both the hierarchical product and the Cartesian product of graphs is introduced and some of its properties are studied. We call it the generalized hierarchical product. In fact, the obtained graphs ...

A graph is walk-regular if the number of closed walks of length rooted at a given vertex is a constant through all the vertices for all . For a walk-regular graph G with d+1 different eigenvalues and spectrally maximum ...

We give a formal definition of a new product of bipartite digraphs, the Manhattan product, and we study some of its main properties. It is shown that when all the factors of the above product are (directed) cycles, then ...

The $n$-dimensional Manhattan network $M_n$---a special case of $n$-regular digraph---is formally defined and some of its structural properties are studied. In particular, it is shown that $M_n$ is a Cayley digraph, ...