On distance-regular graphs with Ki = kj

• Main Author: Garcia, Imelda B.
• Format: text
• Language: English
• Published: Animo Repository 1994
• Subjects: Graph theory; Combinatorial analysis; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/1643; https://animorepository.dlsu.edu.ph/context/etd_masteral/article/8481/viewcontent/TG02363_F_Redacted.pdf
• Institution: De La Salle University

Let be a distance regular graph with diameter d and valency k. For nonnegative integers i and j, with 0 i + j d and vertices u, v E , letki = number of points at distance i from u and kj = number of points at distance j from v. This thesis is a detailed study about distance regular graphs satisfying ki = kj. In particular, it aims to show the following: a. The number of vertices at distance d from any vertex u E is 1.b. The number of points at distance e from u with i , e j, is constant. c. If the number of points at distance j from u is not equal to the number of points at distance (j+1) from u, then the points at distance d from u form a clique for any vertex u E .This thesis is based on the paper of Hiroshi Suzuki entitled On Distance Regular Graphs with Ki = kj.