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TitleLinks between two semisymmetric graphs on 112 vertices via association schemes
Author(s) Mikhail Klin, Josef Lauri, Matan Ziv-Av
TypeArticle in Journal
AbstractThis 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 by-product of the approach presented here, a number of new interesting (mostly non-Schurian) 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.
KeywordsNikolaev graph, Dejter graph, Semisymmetric graph, Ljubljana graph, Double cover, Association scheme, Computer algebra, Deza graph, Overlarge set of designs
URL http://www.sciencedirect.com/science/article/pii/S0747717111002331
JournalJournal of Symbolic Computation
Pages1175 - 1191
NoteSymbolic Computation and its Applications
Translation No
Refereed No