On Delta Graphs and Delta Conjecture

zbMATH Open1398.05125arXiv1610.00792MaRDI QIDQ4962311

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Publication date: 2 November 2018

Abstract: In this paper we define two infinite families of graphs called C-$delta$ graphs and $delta$- graph and prove that $delta$-graphs satisfy $delta$ conjecture. Also we introduce a family of C-$delta$ graphs from which we can identify $delta$ graphs as their complements. Finally we give a list of C-$delta$ graphs and the relationship with their minimum semidefinite rank.

Full work available at URL: https://arxiv.org/abs/1610.00792

zbMATH Keywords

minimum semidefinite rankorthogonal representationdelta conjecturesimple connected graphs\(\delta\)-graph\(C-\delta\) graphs

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Graph algorithms (graph-theoretic aspects) (05C85) Graph operations (line graphs, products, etc.) (05C76)

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