The Second Malta Conference in Graph Theory and Combinatorics 2017 2MCGTC-2017 in honour of the 75th birthday of Professor Stanley Fiorini 26{30 June 2017 ii Welcome Address Mer~ba! We are honoured that you chose to join us for The Second Malta Confer- ence in Graph Theory and Combinatorics. This conference is commemorating the 75th birthday of Professor Stanley Fiorini, who introduced graph theory and combinatorics at the University of Malta. Many of you may be asking when the previous Malta Conference was held? The First Malta Conference on Graphs and Combinatorics was held during the period 28 May { 2 June, 1990, at the Suncrest Hotel, also in Qawra, St Paul's Bay. It differed from a number of similar conferences held in the central Mediterranean region at that time in that it consisted of three types of lectures. L´aszl´oLov´aszand Carsten Thomassen delivered two instructional courses of five one-hour lectures each; the former was A survey of independent sets in graphs and the latter was on Embeddings of graphs. There were also four invited speakers, namely L.W. Beineke, N.L. Biggs, R. Graham and D.J.A. Welsh, each of whom gave a one-hour lecture. The third type of talks were the 20-minute contributed talks running in two parallel sessions and given by 39 speakers. Volume 124 (1994) of the journal Discrete Mathematics was a special edition dedicated to this conference; it was edited by Stanley Fiorini and Josef Lauri, and it consisted of 22 selected papers. Twenty-seven years later we are gathered here for the second such conference organ- ised in the Island of Malta. Although the time-lapse is considerable, the purpose iii of this conference remains the same as that of the first one: to share and discuss a whole spectrum of topics within the interrelated fields of graph theory and com- binatorics. This conference is bringing together almost 200 researchers and mathe- maticians from 46 different countries spread across all the continents, including 14 invited speakers and a special guest of honour. We have received 150 abstracts for 20-minute contributed talks which will run in four parallel sessions and cover a large variety of areas within graph theory and combinatorics. A special issue of Discrete Applied Mathematics dedicated to this conference and containing full-length papers will be published. This Conference was made possible by the support of the University of Malta and through the financial support we received from our sponsors, whom we thank whole- heartedly. We would also like to thank all those who have helped in some way or another to make this Conference possible. Our final words of thanks go to all of you who are gathered here with us on our tiny Island, and we wish you an enjoyable and successful conference here in Qawra, St Paul's Bay. Finally, our gratitude goes to Professor Fiorini, without whose invaluable contribu- tion we would not be here today. Ad multos annos! Peter Borg John Baptist Gauci Josef Lauri Irene Sciriha 18 June 2017 iv Contents Welcome Address iii Professor Stanley Fiorini 1 Short biography . .1 List of Publications in Mathematics . .2 Conference Information 5 Conference Sponsors 7 The Programme 9 Overview . .9 Daily . 10 Monday 26 June 2017 . 10 Tuesday 27 June 2017 . 11 Wednesday 28 June 2017 . 11 Thursday 29 June 2017 . 12 Friday 30 June 2017 . 13 Abstracts of Plenary Talks 15 Alternating Sign Matrices and Hypermatrices (Richard A. Brualdi).... 15 Repetitions in the degree sequence of a graph (Yair Caro)......... 15 The Diameter of Graphs and Digraphs (Peter Dankelmann)........ 18 Graph theoretical models and molecular currents (Patrick Fowler)..... 18 Quantum Walks on Graphs (Chris Godsil).................. 19 On the direct product of finite and infinite graphs (Wilfried Imrich).... 19 A general 2-part Erd}os-Ko-Radotheorem (Gyula O. H. Katona)...... 20 Packing Chromatic Number (Sandi Klavˇzar)................. 20 Introduction to total graph coherent configurations (Mikhail Klin)..... 21 Tiling in High Dimensions (Imre Leader)................... 22 Graph generation and Ramsey numbers (Brendan McKay)......... 22 Cocliques in Derangement Graphs (Karen Meagher)............. 22 Symmetry in graphs and digraphs (Raffaele Scapellato)........... 23 List colourings of hypergraphs (Andrew Thomason)............. 23 v Abstracts of Contributed Talks 25 An application of Hoffman graphs for spectral characterizations of graphs (Aida Abiad)............................... 25 Formation of a giant component in the intersection graph of a random chord diagram (Huseyin Acan)...................... 25 Vertex transitive K¨ahlergraphs whose adjacency operators are commuta- tive (Toshiaki Adachi).......................... 26 Investigating posets via their maximal chains: a Sperner type approach (Seyed Hadi Afzali Borujeni)...................... 27 Baranyai's Theorem for Completeness of Bipartite Induced Subhypergraph (Yasmeen Akhtar)............................ 28 Coherent Graph Partitions (Angela Angeleska)................ 28 Generating theorem of even triangulation on the Klein bottle (Yoshihiro Asayama)................................. 29 Graphs with large vertex and edge reconstruction number (Kevin Joseph Asciak).................................. 30 Localization theorems on Hamilton cycles (Armen Asratian)........ 30 Orthogonal matrices with zero diagonal (Robert Bailey)........... 31 Extremal K5-minor-free graphs with fixed girth (J´anosBar´at)....... 32 Real spectra in non-Hermitian operators (Nat´aliaBebiano)......... 32 Counting Matchings in a class of Fullerene Graphs (Afshin Behmaram).. 33 Minimum Spanning Tree of the Inner Dualist of Honeycomb Graphs (Faqir M. Bhatti)................................. 35 An Equivalence Class Decomposition of Finite Metric Spaces via Gromov Products (Ay¸seH¨umeyra Bilge)..................... 35 Simple Pattern Minimality Problem: two variants and heuristic approaches (Maurizio Boccia)............................. 36 Non-existence of indecomposable 1-factorizations of the complete multi- graph λK2n (Simona Bonvicini)..................... 37 Bipartite graphs in the SSP model of ballistic conduction (Martha Borg). 38 Cross-intersecting families (Peter Borg).................... 39 On the Super Connectivity of Kneser graphs and Johnson graphs (G¨ulnaz Boruzanlı Ekinci)............................. 40 On χ-binding functions for the classes of P5-, 2K2-, and K1;3-free graphs (Christoph Brause)............................ 40 Clique coverings and claw-free graphs (Csilla Bujt´as)............ 41 Exploring soft graphs (Jean-Guy Caputo).................. 42 Generalized connectivity and strong product graph (Roc´ıoM. Casablanca) 43 The Clustered and Bottleneck Clustered Selected-Internal Steiner Tree Problems (Yen Hung Chen)....................... 44 Skolem Labellings of Graphs with Large Chordless Cycles (Nancy E. Clarke) 45 Independent Sets of Families of Graphs via Finite State Automata (Pietro Codara).................................. 45 The Forgotten Topological Index of some Carbon Base Nanomaterials (Ozge¨ C¸olakoˇgluHavare)......................... 46 A construction of regular Hadamard matrices (Dean Crnkovi´c)....... 47 vi The number of P -vertices in a matrix with maximum nullity (Henrique F. da Cruz).................................. 47 On the Mathon bound for regular near hexagons (Bart De Bruyn)..... 48 The Hamilton Cycle Problem for locally traceable and locally Hamiltonian graphs (Johan de Wet).......................... 49 Recent progress on partial difference sets in Abelian groups (Stefaan De Winter).................................. 50 New results on distance spectrum of special classes of trees (Renata Del- Vecchio).................................. 50 Degree Sequences of Hypergraphs, Self-Complementary and Almost Self- Complementary 3-uniform Hypergraphs (Charusheela Deshpande).. 51 The Fibonacci numbers of the composition of graphs (Loiret A. Dosal- Trujillo).................................. 52 2-proper connection of graphs (Trung Duy Doan).............. 53 Restricted size Ramsey numbers for some graphs (Tomasz Dzido)..... 53 Toughness and treewidth (Mark Ellingham)................. 54 Navigating Between Packings of Graphic Sequences (P´eterL. Erd}os)... 54 Autotopism stabilized colouring games on rook's graphs (Ra´ulM. Falc´on) 55 Edge Construction of Molecular NSSDs (Alexander Farrugia)....... 56 Irregular independence and irregular domination (Kurt Fenech)...... 57 Existence theorems for nonnegative integral matrices with given line sums (Ros´arioFernandes)........................... 58 Elementary Derivation of the Hoffman-Singleton Graph and its Automor- phism Group (Jay Fraser)........................ 58 The fixed score tree graph (Juli´anAlberto Fres´an-Figueroa)........ 59 Hypohamiltonian and Hypotraceable Oriented Graphs (Marietjie Frick). 59 Equitable Colorings of l-Corona Products of Cubic Graphs (Hanna Furma´nczyk)............................... 60 Minimal Matrices in the Bruhat Order for Symmetric (0,1)-Matrices (Su- sana Furtado)............................... 61 Resolvable configurations (G´abor G´evay)................... 61 Sufficient conditions for the existence of alternating Hamiltonian paths and cycles in 2-edge-coloured multigraphs (Ilan A. Goldfeder)....... 62 The Edge Intersection Graphs of Paths on a Grid (Martin Charles Golumbic) 62 On the clique number of a strongly regular graph (Gary Greaves)..... 63 Maltese mathematics in the 16th and 17th century (Harald Gropp)..... 64 Orbital matrices and configurations with natural index (Harald Gropp).