The diameter of lifted digraphs
نویسنده
چکیده
The theory of voltage assignments enables one to construct large graphs (directed as well as undirected) as covering spaces of smaller base graphs. All properties of the large graph, called the lift, are determined by the structure of the base graph and by an assignment of voltages (elements of some group) to its arcs. In this paper we prove several upper bounds on the diameter of the lift in terms of some properties of the base graph and the voltage group.
منابع مشابه
From 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 کاملMore 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 کاملClassification of Two-regular Digraphs with Maximum Diameter
The Klee-Quaife problem is finding the minimum order μ(d, c, v) of the (d, c, v) graph, which is a c-vertex connected v-regular graph with diameter d. Many authors contributed finding μ(d, c, v) and they also enumerated and classified the graphs in several cases. This problem is naturally extended to the case of digraphs. So we are interested in the extended Klee-Quaife problem. In this paper, ...
متن کاملOn Quotient Digraphs and Voltage Digraphs
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 t...
متن کاملThe Diameter of Cyclic Kautz Digraphs
A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and degree there is no other digraph with a smaller diameter. This new family is called modified cyclic digraphsMCK(d, ) and it is derived from the Kautz...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 19 شماره
صفحات -
تاریخ انتشار 1999