18 citations · 46 across the 18 of their papers we have counts for
19 papers · 1 filter
Convexity deficit of benzenoids
Nino Bašić, Sarah Berkemer, Jörg Fallmann +6
In 2012, a family of benzenoids was introduced by Cruz, Gutman, and Rada, which they called convex benzenoids. In this paper we introduce the convexity deficit, a new topological i…
Existence of regular nut graphs for degree at most 11
Patrick W. Fowler, John Baptist Gauci, Jan Goedgebeur +2
A nut graph is a singular graph with one-dimensional kernel and corresponding eigenverctor with no zero elements. The problem of determining the orders for which -regular nu…
Existence of Regular Nut Graphs and the Fowler Construction
John Baptist Gauci, Tomaz Pisanski, Irene Sciriha
In this paper the problem of the existence of regular nut graphs is addressed. A generalization of Fowler's Construction which is a local enlargement applied to a vertex in a graph…
Splittable and unsplittable graphs and configurations
Nino Bašić, Jan Grošelj, Branko Grünbaum +1
We prove that there exist infinitely many splittable and also infinitely many unsplittable cyclic configurations. We also present a complete study of trivalent cyclic Haar…
Sizes of Pentagonal Clusters in Fullerenes
Nino Bašić, Gunnar Brinkmann, Patrick W. Fowler +2
Stability and chemistry, both exohedral and endohedral, of fullerenes are critically dependent on the distribution of their obligatory 12 pentagonal faces. It is well known that th…
Coronoids, Patches and Generalised Altans
Nino Bašić, Patrick W. Fowler, Tomaž Pisanski
In this paper we revisit coronoids, in particular multiple coronoids. We consider a mathematical formalisation of the theory of coronoid hydrocarbons that is solely based on incide…