Circuit bases of strongly connected digraphs
نویسندگان
چکیده
The cycle space of a strongly connected graph has a basis consisting of directed circuits. The concept of relevant circuits is introduced as a generalization of the relevant cycles in undirected graphs. A polynomial time algorithm for the computation of a minimum weight directed circuit basis is outlined.
منابع مشابه
On 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 کاملLinear Sphericity Testing of 3-Connected Single Source Digraphs
It has been proved that sphericity testing for digraphs is an NP-complete problem. Here, we investigate sphericity of 3-connected single source digraphs. We provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. Our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $O(n)$ time.
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 کاملSparse highly connected spanning subgraphs in dense directed graphs
Mader (1985) proved that every strongly $k$-connected $n$-vertex digraph contains a strongly $k$-connected spanning subgraph with at most $2kn - 2k^2$ edges, and this is sharp. For dense strongly $k$-connected digraphs, the bound can be significantly improved for dense strongly $k$-connected digraphs. Let $\overline{\Delta}(D)$ be the maximum degree of the complement of the underlying undirecte...
متن کاملInfinite Circulant Digraphs and Random Infinite Circulant Digraphs
In this paper, we completely determine the connectivity of every infinite circulant digraphs and prove that almost all infinite circulant digraphs are infinitely strongly connected and therefore have both oneand two-way infinite Hamiltonian paths.
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:
- Discussiones Mathematicae Graph Theory
دوره 23 شماره
صفحات -
تاریخ انتشار 2003