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  • On the Nullity of Altans and Iterated Altans [Elektronski vir]
    Bašić, Nino
    Altanisation (formation of the altan of a parent structure) originated in the chemical literature as a formal device for constructing generalised coronenes from smaller structures. The altan graph of ... ▫$G$▫, ▫$\mathfrak{a}(G, H)$▫, is constructed from graph ▫$G$▫ by choosing an attachment set ▫$H$▫ from the vertices of ▫$G$▫ and attaching vertices of ▫$H$▫ to alternate vertices of a new perimeter cycle of length ▫$2|H|$▫. We were able to prove sharp bounds for the nullity of altan and iterated altan graphs based on a general parent graph: for any attachment set, the nullity of the altan exceeds the nullity of the parent graph by at most ▫$2$▫. The case of excess nullity ▫$2$▫ had not been noticed before; for benzenoids it occurs first for a parent structure with merely ▫$5$▫ hexagons. We also exhibit an infinite family of convex benzenoids with ▫$3$▫-fold dihedral symmetry (point group ▫$D_{3h}$▫), where nullity increases from ▫$2$▫ to ▫$3$▫ under altanisation. This family accounts for all known examples with the excess nullity of ▫$1$▫ where the parent graph is a singular convex benzenoid.
    Vir: Book of abstracts [Elektronski vir] (Str. 13-14)
    Vrsta gradiva - prispevek na konferenci
    Leto - 2022
    Jezik - angleški
    COBISS.SI-ID - 119814403

    Povezava(-e):

    https://sites.google.com/view/msgt/workshop-on-graph-theory-and-applications/programme/book-of-abstracts?authuser=0

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