強正則圖之研究

Abstract

Friendship定理說明當一個連通圖形滿足任兩點恰有一共同鄰 點時，除了三個點的完全圖之外，此圖必不為正則圖。也就是 說所有c=a=1 的強正則圖只有K3一個。在這篇文章中，我們 從λ的分解來討論一些c=a>1 時的正則圖存在的必要條件， 並且討論如Ramanujan圖及Symplectic圖等屬於該類圖形的一 些性質。除此之外，文章中亦整理了一些c-a值不大的正則 圖。

The friend theorem excludes all strongly regular graphs with c-a=1 except K3. In this thesis, we study some necessary conditions for strongly regular graphs with c-a > 1 based on the decompositions of a, including the families of Ramanujan graphs and symplectic graphs as examples. A survey of strongly regular graphs with small value of c-a were also given in this thesis.