On Quotient Digraphs and Voltage Digraphs
نویسندگان
چکیده
We study the relationship between two key concepts in the theory of digraphs, those of quotient digraphs and voltage digraphs. These techniques contract or expand a given digraph in order to study its characteristics, or obtain more involved structures. As an application, we relate the spectrum of a digraph Γ, called voltage digraph or base, with the spectrum of its lifted digraph Γ. We prove that all the eigenvalues of Γ (including multiplicities) are, in addition, eigenvalues of Γ. This study is carried out by introducing several reduced matrix representations of Γ. As an example of our techniques, we study some basic properties of the Alegre digraph and its base.
منابع مشابه
More skew-equienergetic digraphs
Two digraphs of same order are said to be skew-equienergetic if their skew energies are equal. One of the open problems proposed by Li and Lian was to construct non-cospectral skew-equienergetic digraphs on n vertices. Recently this problem was solved by Ramane et al. In this paper, we give some new methods to construct new skew-equienergetic digraphs.
متن کاملSufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs
Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree and its in-degree . Now let D be a digraph with minimum degree and edge-connectivity If is real number, then the zeroth-order general Randic index is defined by . A digraph is maximally edge-connected if . In this paper we present sufficient condi...
متن کاملOn spectral radius of strongly connected digraphs
It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.
متن کاملVertex Removable Cycles of Graphs and Digraphs
In this paper we defined the vertex removable cycle in respect of the following, if $F$ is a class of graphs(digraphs) satisfying certain property, $G in F $, the cycle $C$ in $G$ is called vertex removable if $G-V(C)in in F $. The vertex removable cycles of eulerian graphs are studied. We also characterize the edge removable cycles of regular graphs(digraphs).
متن کاملFrom expanded digraphs to lifts of voltage digraphs and line digraphs∗
In this note we present a general approach to construct large digraphs from small ones. These are called expanded digraphs, and, as particular cases, we show the close relationship between lifted digraphs of voltage digraphs and line digraphs, which are two known ways to obtain dense digraphs. In the same context, we show the equivalence between the vertex-splitting and partial line digraph tec...
متن کامل