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Title: | Two-graphs and NSSDs : an algebraic approach |
Authors: | Sciriha, Irene Collins, Luke |
Keywords: | Graph theory Mathematics Eigenvalues Nullity |
Issue Date: | 2019 |
Publisher: | Elsevier |
Citation: | Sciriha, I., & Collins, L. (2019). Two-graphs and NSSDs: An algebraic approach. Discrete Applied Mathematics, 266, 92-102. |
Abstract: | A two-graph (V, ∆) is a combinatorial entity consisting of a set V together with a collection ∆ of unordered triples of elements of V, such that there exists a graph G with vertex set V in which the triples in ∆ are precisely the subgraphs K3 or K2∪ ̇ K1 induced in G. Switching is an equivalence relation partitioning the graphs on n vertices into switching classes. All the graphs that are switching equivalent to G yield the same ∆ and therefore the two–graph (V, ∆) is taken to consist of the graphs in the switching class of G. The graphs in a switching class have similar (0, ±1)-Seidel matrices. So the spectrum of (V, ∆) is taken as the Seidel spectrum of a graph in the switching class. The two graphs with exactly two distinct Seidel eigenvalues μ1, μ2 are regular. We show how an involution M(μ1, μ2) provides a simple way to determine structural and combinatorial properties of the graphs of a regular two- graph. If μ1 + μ2 = 0, the regular two-graph consists of conference graphs. We show that M(μ1, −μ1) is an NSSD (non-singular graph with a singular deck) with the special property of being a nutful graph. The rich properties of a nutful NSSD reveal new spectral properties of conference graphs. |
URI: | https://www.um.edu.mt/library/oar/handle/123456789/65151 |
Appears in Collections: | Scholarly Works - FacSciMat |
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SciLukeCollinsConfGr20178.pdf Restricted Access | 351.21 kB | Adobe PDF | View/Open Request a copy |
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