Coalesced and embedded nut graphs in singular graphs

Irene Sciriha

Abstract


A nut graph has a non-invertible (singular) 0-1 adjacency matrix with non-zero entries in every kernel eigenvector. We investigate how the concept of nut graphs emerges as an underlying theme in the theory of singular graphs. It is known that minimal configurations (MCs) are necessarily found as subgraphs of singular graphs. We construct MCs having nut graphs as subgraphs. Nut graphs can be coalesced with singular graphs at particular vertices or grown into a family of core graphs of larger nullity by adding a vertex at a time. Moreover, we propose a construction of nut line graph of trees by coalescence and a local enlargement of nut fullerenes and tetravalent nut graphs.


Keywords


adjacency matrix, nut fullerenes, eigenvectors

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DOI: https://doi.org/10.26493/1855-3974.20.7cc

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications