TAILIEUCHUNG - Báo cáo toán học: "On the Graphs of Hoffman-Singleton and Higman-Sims"

Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: On the Graphs of Hoffman-Singleton and Higman-Sims. | On the Graphs of Hoffman-Singleton and Higman-Sims Paul R. Hafner Department of Mathematics University of Auckland Auckland New Zealand hafner@ Submitted Mar 2 2004 Accepted Aug 27 2004 Published Nov 3 2004 MR Subject Classifications 05C62 05C25 05B25 51E10 51E26 Keywords Hoffman-Singleton graph Higman-Sims graph Higman-Sims group biaffine plane S 3 6 22 Abstract We propose a new elementary definition of the Higman-Sims graph in which the 100 vertices are parametrised with Z4 X Z5 X Z5 and adjacencies are described by linear and quadratic equations. This definition extends Robertson s pentagonpentagram definition of the Hoffman-Singleton graph and is obtained by studying maximum cocliques of the Hoffman-Singleton graph in Robertson s parametrisation. The new description is used to count the 704 Hoffman-Singleton subgraphs in the Higman-Sims graph and to describe the two orbits of the simple group HS on them including a description of the doubly transitive action of HS within the Higman-Sims graph. Numerous geometric connections are pointed out. As a by-product we also have a new construction of the Steiner system S 3 6 22 . 1 Introduction The Higman-Sims graph is the unique strongly regular graph whose parameters are 100 22 0 6 . it is a graph of order 100 regular of degree 22 it is triangle-free any two adjacent vertices have 0 common neighbours and any two non-adjacent vertices have exactly 6 neighbours in common. This graph made its first official appearance 23 in the context of the construction of the sporadic simple group HS which is a subgroup of index 2 in the automorphism group of the graph note Section 13 for a comment on the history . In this paper we provide a new and elementary construction of the Higman-Sims graph combining a geometric interpretation 16 of Robertson s pentagon-pentagram construction of the Hoffman-Singleton graph with the known construction of the Higman-Sims THE ELECTRONIC JOURNAL OF COMBINATORICS 11 2004 R77 1 .

TÀI LIỆU LIÊN QUAN
TỪ KHÓA LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
9    210    0    29-03-2024
34    199    1    29-03-2024
20    242    2    29-03-2024
14    160    0    29-03-2024
20    189    2    29-03-2024
15    176    0    29-03-2024
23    147    0    29-03-2024
37    146    0    29-03-2024
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.