Kernels in Cartesian products of digraphs

نویسندگان

  • R. Lakshmi
  • S. Vidhyapriya
چکیده

A kernel J of a digraph D is an independent set of vertices of D such that for every vertex w ∈ V (D)\J there exists an arc from w to a vertex in J . In this paper we have obtained results for the existence and nonexistence of kernels in Cartesian products of certain families of digraphs, and characterized T Cn, T Pn and Cm Cn which have kernels, where T is a tournament, and Pn and Cn are, respectively, the directed path and the directed cycle of order n. Finally, we have introduced and studied kernel-partitionable digraphs.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Exponents of Cartesian Products of Two Digraphs of Special Orders

In this paper, we find the maximum exponent of D × E, the cartesian product of two digraphs D and E on n, n + 2 vertices, respectively for an even integer n ≥ 4. We also characterize the extremal cases.

متن کامل

On the Cartesian skeleton and the factorization of the strong product of digraphs

The three standard products (the Cartesian, the direct and the strong product) of undirected graphs have been wellinvestigated, unique prime factor decomposition (PFD) are known and polynomial time algorithms have been established for determining the prime factors. For directed graphs, unique PFD results with respect to the standard products are known. However, there is still a lack of algorith...

متن کامل

Connectivity of Cartesian product graphs

Use vi , i , i , i to denote order, connectivity, edge-connectivity and minimum degree of a graphGi for i=1, 2, respectively. For the connectivity and the edge-connectivity of the Cartesian product graph, up to now, the best results are (G1×G2) 1+ 2 and (G1×G2) 1+ 2. This paper improves these results by proving that (G1×G2) min{ 1+ 2, 2+ 1} and (G1×G2)= min{ 1+ 2, 1v2, 2v1} ifG1 andG2 are conne...

متن کامل

2-distance-transitive Digraphs Preserving a Cartesian Decomposition

In this paper, we study 2-distance-transitive digraphs admitting a cartesian decomposition of their vertex set.

متن کامل

On the existence of (k, l)-kernels in infinite digraphs: A survey

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent (if u, v ∈ N , u 6= v, then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l) set of vertices. A k-kernel is a (k, k− 1)-kernel. This work is a survey of results proving sufficient conditions for the exist...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Australasian J. Combinatorics

دوره 66  شماره 

صفحات  -

تاریخ انتشار 2016