Wiener numbers of benzenoid hydrocarbons: two theorems |
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| Institution: | 1. University of California at Merced, Merced, CA 95344, USA;2. Ethel Percy Andrus Gerontology Center, Leonard Davis School of Gerontology, University of Southern California, Los Angeles, CA 90089, USA;3. Departamento de Bioquímica, Instituto de Química, Universidade de São Paulo, São Paulo, SP, Brazil;4. German Institute of Human Nutrition, Potsdam-Rehbrücke, Nuthetal, Germany;5. Division of Neonatology, Department of Pediatrics, Children׳sHospital of Philadelphia;6. Department of Biophysics and Free Radical Research Center, Medical College of Wisconsin, Milwaukee, WI 53226, USA;7. Department of Pediatrics, Perelman School of Medicine, University of Pennsylvania,Philadelphia, PA 19104, USA;8. Cardiovascular Division, British Heart Foundation Centre of Research Excellence, King׳s College London, London SE1 9NH, UK;9. Departamento de Bioquímica, Facultad de Medicina, Universidad de la República, 11800 Montevideo, Uruguay;10. Department of Pharmacology, Vanderbilt University, Nashville, TN 37240, USA;11. Department of Physiology, Faculty of Medicine, Universitat de València, Valencia, Spain;12. Division of Molecular & Computational Biology, Department of Biological Sciences, Dornsife College of Letters, Arts, and Sciences, University of Southern California, Los Angeles, CA 90089, USA;1. Bone Physiopathology Group, Multifactorial Disease and Complex Phenotype Research Area, Bambino Gesù Children’s Hospital, Rome, Italy;2. Rare Diseases and Medical Genetic Unit, Bambino Gesù Children''s Hospital, Rome, Italy;3. Department of Pediatric Hematology and Oncology, Bambino Gesù Children''s Hospital, Rome, Italy;4. Research Laboratories, Bambino Gesù Children''s Hospital, Rome, Italy;5. Villa Aurora” Clinic, Rome, Italy;6. Clinical Laboratory, Bambino Gesù Children’s Hospital, Rome, Italy;7. Histopathology, Bambino Gesù Children''s Hospital, Rome, Italy;8. Division of Immunology and Infectious Diseases Department of Pediatrics, Bambino Gesù Children Hospital, Rome, Italy;1. Institute of Biosciences and Bio-Resources, National Research Council (CNR-IBBR), 80100, Naples, Italy;2. IRCCS Neuromed, 86077, Pozzilli, IS, Italy;3. Department of Environmental and Biological Sciences and Technologies, University of Salento, 73100, Lecce, Italy;4. Institute of Food Sciences, National Research Council (CNR-ISA), 83100, Avellino, Italy |
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| Abstract: | Two exact results on the Wiener numbers of catacondensed benzenoid hydrocarbons are obtained. All catacondensed isomers have Wiener numbers congruent modulo 8. Among unbranched catacondensed systems, helicenes have the minimum and linear polyacenes the maximum Wiener number. |
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