Forwarding and optical indices of a graph

نویسنده

  • Adrian Kosowski
چکیده

Motivated by wavelength-assignment problems for all-to-all traffic in optical networks, we study graph parameters related to sets of paths connecting all pairs of vertices. We consider sets of both undirected and directed paths, under minimisation criteria known as edge congestion and wavelength count; this gives rise to four parameters of a graph G: its edge forwarding index π(G), arc forwarding index E π(G), undirected optical index w(G), and directed optical index E w(G). In the paper we address two long-standing open problems: whether the equality E π(G) = E w(G) holds for all graphs, and whether indices π(G) and w(G) are hard to compute. For the first problem, we give an example of a family of planar graphs {Gk} such that E π(Gk) 6= E w(Gk). For the second problem, we show that determining either π(G) or w(G) is NP-hard. © 2008 Elsevier B.V. All rights reserved.

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

THE UNDIRECTED OPTICAL INDICES OF COMPLETE m-ARY TREES

The routing and wavelength assignment problem arises from the investigation of optimal wavelength allocation in an optical network that employs Wavelength Division Multiplexing (WDM). Consider an optical network that is represented by a connected, simple graph G. An all-to-all routing R in G is a set of paths connecting all pairs of vertices of G. The undirected optical index of G is the minimu...

متن کامل

Expanding and Forwarding

Expanding parameters of graphs (magnification constant, edge and vertex cutset expansion) are related by very simple inequalities to forwarding parameters (edge and vertex forwarding indices). This shows that certain graphs have eccentricity close to the diameter. Connections between the forwarding indices and algebraic parameters like the smallest eigenvalue of the Laplacian or the genus of th...

متن کامل

Forwarding indices of folded n-cubes

For a given connected graph G of order n, a routing R is a set of n(n − 1) elementary paths specified for every ordered pair of vertices in G. The vertex (resp. edge) forwarding index of a graph is the maximum number of paths of R passing through any vertex (resp. edge) in the graph. In this paper, the authors determine the vertex and the edge forwarding indices of a folded n-cube as (n− 1)2n−1...

متن کامل

The Forwarding Indices of Graphs -- a Survey

A routing R of a given connected graph G of order n is a collection of n(n−1) simple paths connecting every ordered pair of vertices of G. The vertexforwarding index ξ(G,R) of G with respect to R is defined as the maximum number of paths in R passing through any vertex of G. The vertex-forwarding index ξ(G) of G is defined as the minimum ξ(G,R) over all routing R’s of G. Similarly, the edge-for...

متن کامل

The Merrifield-Simmons indices and Hosoya indices of some classes of cartesian graph product

The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we give formula for Merrifield-Simmons and Hosoya indices of some classes of cartesian product of two graphs K{_2}×H, where H is a path graph P{_n}, cyclic graph C{_n}, or star gra...

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:
  • Discrete Applied Mathematics

دوره 157  شماره 

صفحات  -

تاریخ انتشار 2009