On some properties of a fixed-degree cayley graph from linear group = 고정된 분지수를 갖는 선형 그룹 케일리 그래프의 성질에 관한 연구

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Cayley graph is a mathematical model in which all vertices and edges are represented as elements of a finite group $G$ and relations between the elements with respect to some generating set $S$ of $G$. Since the model is based on rich background of group theory, it has many advantages: the symmetric structures in any Cayley graph make itself preferable as a static interconnection network. Furthermore, sensible choice of its basis group and corresponding generating set can add more desirable properties. So it is widely used in designing and analyzing interconnection networks. This thesis proposes a new class of Cayley graph based on the linear group $\mbox{PSL}(2,p)$ for a prime power integer $p$, and considers some of its properties. The graph has $O(p^3)$ nodes and fixed degree 3. Similar to the structure of cube-connected cycle, it consists of interconnected cycles. We show some additional properties of the graph. It is planar for $p=3,5$ and has maximum connectivity. The hamiltonicity of the graph is also considered. Finally, a simple routing algorithm on the graph is developed, which bounds the diameter of the graph to $O(\sqrt[3]{|V|})$. By experimental results, we conjecture that the diameter of the graph is $O(\log |V|)$ in optimum.
Advisors
Chwa, Kyung-Yongresearcher좌경룡researcher
Description
한국과학기술원 : 전산학과,
Publisher
한국과학기술원
Issue Date
1996
Identifier
106041/325007 / 000943483
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 전산학과, 1996.2, [ i, 45 p. ]

Keywords

Linear group; Cayley graph; Interconnection networks; 상호 연결망; 선형 그룹; 케일리 그래프

URI
http://hdl.handle.net/10203/34151
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=106041&flag=dissertation
Appears in Collection
CS-Theses_Master(석사논문)
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