A Moore-like Bound for Graphs of Diameter 2 and given Degree, Obtained as Abelian Lifts of Dipoles
نویسنده
چکیده
In this note we prove a Moore-like bound for graphs of diameter two and given degree which arise as lifts of dipoles with loops and multiple edges, with voltage assignments in Abelian groups.
منابع مشابه
An upper bound for graphs of diameter 3 and given degree obtained as abelian lifts of dipoles
We derive an upper bound on the number of vertices in graphs of diameter 3 and given degree arising from Abelian lifts of dipoles with loops and multiple edges.
متن کاملLarge vertex-transitive and Cayley graphs with given degree and diameter
We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that arise as lifts of dipoles with voltage assignments in Abelian groups. Further, we construct a family of Cayley graphs of degree d = 3m− 1 and diameter k ≥ 3 of order kmk. By comparison with other available results in this area we show that, for sufficiently large d and k such that k ≤ d − 2, our fa...
متن کاملA Moore-like bound for mixed abelian Cayley graphs
We give an upper bound for the number of vertices in mixed abelian Cayley graphs with given degree and diameter.
متن کاملPhD Thesis: Topology of Interconnection Networks with Given Degree and Diameter
In this thesis I deal with the design of optimal interconnection networks. Optimality is interpreted as the largest possible number of nodes in the network, under given constraints on the number of connections attached to a node (degree of the node), and on the length of shortest paths between any two nodes (diameter of the network). Any interconnection network with bidirectional channels can b...
متن کاملDiameter Two Graphs of Minimum Order with Given Degree Set
The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003