New largest known graphs of diameter 6
نویسندگان
چکیده
In the pursuit of obtaining largest graphs of given maximum degree ∆ and diameter D, many construction techniques have been developed. Compounding of graphs is one such technique. In this paper, by means of the compounding of complete graphs into a Moore bipartite graph of diameter 6, we obtain a family of large graphs of the same diameter. For ∗Research supported in part by the Australian Research Council grant ARC DP0450294, by the Spanish Ministry of Education under the project MTM2005-08990-C02-01 and by the Catalan Research Council under the project 2005SGR00256. †[email protected] ‡[email protected] §[email protected] ¶[email protected]
منابع مشابه
Constructions of Large Graphs on Surfaces
We consider the degree/diameter problem for graphs embedded in a surface, namely, given a surface Σ and integers ∆ and k, determine the maximum order N(∆, k,Σ) of a graph embeddable in Σ with maximum degree ∆ and diameter k. We introduce a number of constructions which produce many new largest known planar and toroidal graphs. We record all these graphs in the available tables of largest known ...
متن کاملNew Large Graphs with Given Degree and Diameter
In this paper we give graphs with the largest known order for a given degree ∆ and diameter D. The graphs are constructed from Moore bipartite graphs by replacement of some vertices by adequate structures. The paper also contains the latest version of the (∆, D) table for graphs.
متن کاملAn Overview of the Degree/Diameter Problem for Directed, Undirected and Mixed Graphs
A well-known fundamental problem in extremal graph theory is the degree/diameter problem, which is to determine the largest (in terms of the number of vertices) graphs or digraphs or mixed graphs of given maximum degree, respectively, maximum outdegree, respectively, mixed degree; and given diameter. General upper bounds, called Moore bounds, exist for the largest possible order of such graphs,...
متن کاملOn Large Graphs with Given Degree and Diameter
The degree/diameter problem is to determine the largest possible number of vertices in a graph of given maximum degree and given diameter. It is well known that the general upper bound, called Moore bound, for the order of such graphs is attainable only for certain special values of degree and diameter. Finding better upper bounds for the maximum possible number of vertices, given the other two...
متن کاملNew record graphs in the degree-diameter problem
In 1994, Dinneen and Hafner (Networks 24 No. 7, 359–367) published a table of largest orders of graphs of given degree up to 15 and diameter up to 10, known to that date. The table also contained 48 new values found by the authors with the help of computer searches over Cayley graphs of semidirect products of (mostly) cyclic groups. Prior to our work, only relatively few values in the table hav...
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:
- Networks
دوره 53 شماره
صفحات -
تاریخ انتشار 2009