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https://www.um.edu.mt/library/oar/handle/123456789/28360
Title: | Non-singular graphs with a singular deck |
Authors: | Farrugia, Alexander Gauci, John Baptist Sciriha, Irene |
Keywords: | Mathematics -- Charts, diagrams, etc. Mathematics -- Problems, exercises, etc. |
Issue Date: | 2016 |
Publisher: | Elsevier BV |
Citation: | Farrugia, A., Gauci, J. B., & Sciriha, I. (2016). Non-singular graphs with a singular deck. Discrete Applied Mathematics, 202, 50-57. |
Abstract: | The n-vertex graph G(= Γ (G)) with a non-singular real symmetric adjacency matrix G, having a zero diagonal and singular (n−1)×(n−1) principal submatrices is termed a NSSD, a Non-Singular graph with a Singular Deck. NSSDs arose in the study of the polynomial reconstruction problem and were later found to characterise non-singular molecular graphs that are distinct omni-conductors and ipso omni-insulators. Since both matrices G and G−1 represent NSSDs Γ (G) and Γ (G−1), the value of the nullity of a one-, two and three-vertex deleted subgraph of G is shown to be determined by the corresponding subgraph in Γ (G−1). Constructions of infinite subfamilies of non-NSSDs are presented. NSSDs with all two-vertex deleted subgraphs having a common value of the nullity are referred to as G-nutful graphs. We show that their minimum vertex degree is at least 4. |
URI: | https://www.um.edu.mt/library/oar//handle/123456789/28360 |
Appears in Collections: | Scholarly Works - FacSciMat Scholarly Works - JCMath |
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Non-Singular_graphs_with_a_Singular_Deck_2016.PDF Restricted Access | 465.53 kB | Adobe PDF | View/Open Request a copy |
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