Titles & Abstracts
Keynote Speakers
Gilles Caporossi, "AutoGraphiX 1 to 3: 15 years of Variable Neighborhood Search for Extremal Graphs"
Abstract. If the AutoGraphiX (AGX) system development started in 1997 during G. Caporossi’s Ph.D. thesis and the first paper describing the system appeared in 2000. Using the Variable Neighborhood Search (VNS), the main goal of AGX is to find extremal graphs which may be used for various purposes, such as finding refutations of conjectures or finding new ones. The first version of AGX was a prototype, a proof of concept, that was used privately between 1997 and 2001. Shortly after, the AGX-2 system was developed and made freely available in 2005. It was the occasion to improve the optimizer and make it easier to use. Ten years after AGX was made available to public, a new version is proposed. The difference between AGX-2 and AGX-III is not just a number. The whole system was completely rewritten from scratch taking advantage of the experience from the years using the previous versions. If the main principle underlying AGX, the optimization, is still at the center of the system, most of it was renewed, including the interface and the way to consider the problem. Among the differences, let’s mention its capability to natively handle vertex related values and multiobjective optimization.
In this talk, we will start by a brief history of the system and the main results obtained. We will continue with an overview of the new system and explain how to get the most of it for research.
Remi Chauvin, "From chemistry to maths: from spectroscopy to spectral graph theory, from aromatic compounds to 'aromatic graphs' "
Michel Deza, "Extended family of fullerenes"
Matthias Ernzerhof, "Simple theories for conjugated π-electron systems"
Abstract. Since the early days of chemistry delocalized π-electron systems received heightened attention. More recently, physicists started to share this interest and increasingly new phenomena are reported in structures that derive from graphene. Starting from the Hückel Hamiltonian, we perform [1] a unitary transformation and obtain a quasi-relativistic matrix Hamiltonian, relating the physicists’ models of graphene to the chemists’ ones. Drawing on this work, we discuss electron transport in nano-graphenes (NGs), which are finite fragments of graphene. We describe a simple theory [2, 3] for ballistic electron transport through NGs which enables us to establish relations between structure and conductance and we compare the predictions to experiment. An extension [4] of our approach to multichannel problems is developed which relies on an eigenchannel description of the conducting states of the device. Finally, we turn to molecular photovoltaic cells [5]. Electron transport through π-electron systems is described by a coherent transport mechanism where a wave function extends from the left contact over the molecule to the right contact. The addition of a photon absorption process in the molecule results in a molecular photovoltaic cell, where the photon energy is converted into electronic energy. A theoretical model for this energy conversion is presented and applied to generic molecular photovoltaic devices.
 [1] Ernzerhof, Goyer, JCTC 6, 1818 (2010).
[2] Mayou, Zhou, Ernzerhof, JPC C117, 7870 (2013).
[3] Ernzerhof, JCP 140, 114708 (2014).
[4] Rocheleau, Ernzerhof JCP 137, 174112 (2012).
[5] Ernzerhof, Mayou, Bélanger, in preparation.
Elizabeth Hartung, "The Clar and Fries Numbers of Fullerenes and Benzenoids"
Abstract. Fullerenes model carbon molecules and are plane trivalent graphs with only hexagonal and pentagonal faces. Benzenoids, or graphene patches, are graphs with vertices of degree 2 or 3 where all interior faces are hexagons. The Clar and Fries numbers are two parameters of these graphs thought to predict the stability of these molecules. We will discuss various results on these topics.
Purusottam Jena, " Many Faces of Carbon"
Douglas Klein, "Conjugated-Carbon Nano-Structure"
Tomaž Pisanski, "Conjugated Circuits Applied to Iterated Altans, Ring Currents, and Resonance Graphs"
The concept of conjugated circuits is revisited from a mathematical stand-point. Some classical results are explained and some applications and computations are presented. In particular, iterated altans, ring currents, and resonance graphs are considered. Joint work with Patrick Fowler (University of Sheffield), Wendy Myrvold (University of Victoria), Nino Bašić (University of Ljubljana).
Stan Schein, "Caps from icosahedral fullerenes, indices of their nanotubes and bonding patterns"
Abstract. With Gunnar Brinkmann (University of Ghent). Both carbon nanotubes and icosahedral fullerenes may be specified by a pair of indices that describe a vector in a tiling of hexagons. For a nanotube, the vector (n,m) describes its circumference and its structure [zigzag (n,0), armchair (n,n) or chiral (n¹m)]. In addition, if (n-m) is divisible by 3, the tube is metallic; if not, it is a semiconductor. For an icosahedral fullerene, the vector (h,k) describes its spacing of pentagons and its structure [achiral (h,0), achiral (h,h) or chiral (h¹k)] In addition, divisibility of (h-k) by 3 (or not) controls bonding patterns. It is known that different caps carved from the icosahedral fullerene CÂ60, with (h,k) = (1,1) and (h-k) divisible by 3, may be fit by nanotubes with different (n,m) [e.g., (9,0), (5,5) and (8,2)] with (n-m) also divisible by 3. Here, from formulas we develop for (n,m) for each of five types of cap carved from any icosahedral fullerene (h,k), we find that the converse is true, that one nanotube (n,m) may fit caps from icosahedral fullerenes with more than one (h,k). However, tube (n-m) and cap (h-k) may or may not agree with regard to divisibility by 3, with consequences for bonding patterns. We look forward to discussion of possible uses for these different types of cap1/nanotube/cap2. Picture link.
Nico Van Cleemput, "Classification and generation of nanocones"
Abstract. Nanocones are carbon networks conceptually situated in between graphite and the famous fullerene nanotubes. Graphite is a planar carbon network where each atom has three neighbours and the faces formed are all hexagons. Fullerene nanotubes are discussed in two forms: once the finite, closed version where except for hexagons you have 12 pentagons and once the one-side infinite version where 6 pentagons bend the molecule so that an infinite tube with constant diameter is formed. A nanocone conceptually lies between graphite and one-side infinite fullerene nanotubes: next to hexagons it has between 1 and 5 pentagons, so that neither the flat shape of graphite nor the constant diameter tube of the nanotubes can be formed. The structure of graphite is uniquely determined, but for nanotubes and nanocones an infinite variety of possibilities exist. There already exist fast algorithms to generate fullerene nanotubes that are, e.g., used to detect energetically possible nanotubes. In this talk we describe a classification result and a generator for nanocones.
Contributed Talks
Laimutis Bytautas , "Novel Developments in ab initio Quantum Chemistry Methodology with Applications"
Ratko Darda, "Trees of Given Order and Independence Number with Minimal First Zagreb Index"
Abstract. In this talk I will give the characterization of extremal trees with the minimal first Zagreb index among trees of order n and the independence number α, solving one of open problems of Das, Xu and Gutman asked in [MATCH Commun. Math. Comput. Chem. 70 (2013),301-314].
Patrick Fowler, "Ring Currents and aromaticity"
Abstract. I will talk about currents induced in aromatic molecules by external magnetic fields, why chemists are interested in them, how we can now calculate them, and how graph theory can be used to enrich chemical understanding and give new insights into the patterns obtained. Simple models for current divide into those based on spectral graph theory (in the form of Huckel and Huckel London theory) or on the theory of matchings (in the form of Conjugated Circuit models). Both have advantages and disadvantages, as will be discussed. This talk includes joint work with Wendy Myrvold
Scott Gronert, "Experimental and Computational Studies of C-H Bond Activation of Hydrocarbons by a Cationic Iridium (III) Dichloride Phenanthroline Complex"
Abstract. With Christopher A. Swift (VCU Department of Chemistry). The conversion of hydrocarbons to molecules with useful functional groups is a key objective in synthetic chemistry. The high stability of hydrocarbons, particularly aromatic species, has made functionalization difficult and a limited set of technologies is available. Conceptually, modification of carbon-hydrogen bonds in these species is very attractive and has been an area of intense research effort. The process has been called C-H activation. In the present study, we describe a combined gas-phase experimental and computational study of a new iridium species that is capable of modifying C-H bonds in hydrocarbons. The computational work on cyclohexane and toluene reveals a novel, concerted mechanism that avoids a conventional oxidative-addition intermediate. We also have examined the reactions of the catalyst with several other substrates and modeled the systems computationally.
Jennifer Jordan, "Similarity and a New Duality for Fullerenes"
Abstract. With Jack Graver (Syracuse University). Fullerene signatures can be used to define a classification of similar fullerenes in which two fullerenes are similar if the Coexeter coordinates of each edge in the signature of one is a rational multiple of the corresponding Coexeter coordinate in the other. In this way, the collection of all fullerenes can be partitioned into equivalence classes of similar signatures. The classes can be labeled as leapfrog type or non-leapfrog type by examining the structure of the most reduced signature in the class. Furthermore, if we leapfrog any fullerene we get a new fullerene distinct up to similarity.
Performing the leapfrog construction a second time returns us to a fullerene in the similarity class of the original structure. This yields a duality between similarity classes that links a class of leapfrog fullerenes with a class of non-leapfrog ones.
Klavdija Kutnar, "On Existence of Odd Automorphisms in Vertex-Transitive Graphs"
Abstract. A graph is said to be vertex-transitive if its automorphism group is acting transitively on the set of its vertices. We will give an overview of the various results relative to the concept of even/odd automorphisms of vertex-transitive graphs, that is, even/odd permutations preserving the structure of the graph in question. (Joint work with Dragan Marusic.)
Craig Larson, "Automated Conjecture-Making"
Abstract. A program that can generate invariant-relation and property-relation conjectures for a wide variety of objects including, for instance, fullerenes and benzenoids will be introduced, together with many examples. This is joint work with Nico Van Cleemput.
Dieter Mourisse, "The generation of nanojoins"
Andrey Rukhin, "Accelerated 3x + 1 Minimum-Inverse Map"
Wendy Myrvold, "Graph Theoretic Models of Ring Currents"
Various graph theoretic approaches have been proposed for modelling ring currents in benzenoids. We compare these to each other and discuss the situations where they do not provide nice predictions. Insight gained by using Aihara's approach for breaking currents from Huckel-London computations into individual cycle contributions is used to develop proposals for new graph theoretic current models that unlike the standard approaches can also predict currents in benzenoids with no perfect matchings. This is joint work with Patrick Fowler, Joe Clarke, Sam Cotton, Dan Jenkinson, and Magda Sroka (Univ. of Sheffield), and Bill Bird, Matthew Imrie, and Parminder Kaur (Univ. of Victoria).
Vladimir Rosenfeld, "Borane Polyhedra as Building Blocks for Unknown but Potentially Isolatable New Molecules – Extensions based on Computations of the Known B18H22 Isomers"
Dong Ye, "Graph Inverses and Median Eigenvalues"
Abstract. Let $(G,\omega) be a weighted graph with a weight-function $\omega: E(G)\to \mathbb R$. A weighted graph $(G,\omega)$ is invertible to a new weighted graph if its adjacency matrix is invertible. A graph inverse can be applied to bound median eigenvalues of a graph and therefore the HOMO-LUMO gaps of graphs. In this paper, we characterize the inverse of a weighted graph based on its Sachs subgraphs that are spanning subgraphs with only $K_2$ or cycles (or loops) as components. A characterization of graphs with a unique Sachs subgraph is obtained. For these graphs with a unique Sachs subgraph, we show their spectra have half positive eigenvalues and half negative eigenvalues if they have a perfect matching. As applications, we show that the median eigenvalues of stellated graphs of trees and corona graphs belong to different halves of the interval $[-1,1]$. This is joint work with Y. Yang, B. Mandal and D.J. Klein.
