Details:
Title  Links between two semisymmetric graphs on 112 vertices via association schemes  Author(s)  Mikhail Klin, Josef Lauri, Matan ZivAv  Type  Article in Journal  Abstract  This paper provides a model of the use of computer algebra experimentation in algebraic graph theory. Starting from the semisymmetric cubic graph L on 112 vertices, we embed it into another semisymmetric graph N of valency 15 on the same vertex set. In order to consider systematically the links between L and N , a number of combinatorial structures are involved and related coherent configurations are investigated. In particular, the construction of the incidence double cover of directed graphs is exploited. As a natural byproduct of the approach presented here, a number of new interesting (mostly nonSchurian) association schemes on 56, 112 and 120 vertices are introduced and briefly discussed. We use computer algebra system GAP (including GRAPE and nauty), as well as computer package COCO.  Keywords  Nikolaev graph, Dejter graph, Semisymmetric graph, Ljubljana graph, Double cover, Association scheme, Computer algebra, Deza graph, Overlarge set of designs  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111002331 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  10  Pages  1175  1191  Year  2012  Note  Symbolic Computation and its Applications  Edition  0  Translation 
No  Refereed 
No 
