Abstract
The article reports investigations of the “topological” properties of benzenoid molecules which the author has performed in the last 20 years. Emphasis is given on recent developments and other scientists' contributions to these researches. Topics covered in recent books and reviews are avoided. The article outlines spectral properties, some aspects of the study of Kekulé and Clar structures, the Wiener index as well as a number of graphs derived from benzenoid systems (inner dual, excised internal structure, Clar graph, Gutman tree, coral and its dual).
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Dewar MJS, Longuet-Higgins HC (1952) Proc Roy Soc London A214: 482
Gutman I (1974) Croat Chem Acta 46: 209
Gutman I, Cyvin SJ (1989) Introduction to the theory of benzenoid hydrocarbons, Springer, Berlin Heidelberg New York
Merrifield RE, Simmons HE (1989) Topological methods in chemistry, Wiley, New York
Gutman I, Cyvin SJ (eds) (1990) Advances in the theory of benzenoid hydrocarbons, (Topics in Current Chemistry 153), Springer, Berlin Heidelberg New York
Cvetković D, Gutman I, Trinajstić N (1974) J Chem Phys 61: 2700
He WC, He WJ (1986) Theor Chim Acta 70: 447
He WJ, He WC (1989) Theor Chim Acta 75: 389
Sheng RQ (1989) Math Chem 24: 201
Gutman I, Cyvin SJ (1989) J Mol Struct (Theochem) 184: 159
Gutman I (1983) In: Cvetković D, Gutman I, Pisanski T, Tošić R (Eds) Graph theory, Univ Novi Sad, Novi Sad, pp 151–160
Kirby EC (1990) J Math Chem 4: 31
Kirby EC (1990) J Chem Soc Faraday Trans 86: 447
Cvetković D, Gutman I (1981) Publ Inst Math (Beograd) 29: 49
Gutman I, Mallion RB, Essam JW (1983) Molec Phys 50: 859
John P, Sachs H (1990) J Chem Soc Faraday Trans 86: 1033
John P, Sachs H (1990) Topics Curr Chem 153: 145
Dias JR (1984) J Chem Inf Comput Sci 24: 124
Dias JR (1984) Canad J Chem 62: 2914
Dias JR (1989) Z Naturforsch 44a: 765
Dias JR (1987) Handbook of polycyclic hydrocarbons Part A Benzenoid hydrocarbons, Elsevier, Amsterdam
Gutman I, Dias JR (1990) In: Bodendiek R (ed) Contemporary methods in graph theory, BI-Wissenschaftsverlag, Mannheim, pp 249–259
Gutman I, Kirby EC (1991) Math Chem 26: 111
Gutman I, Polansky OE (1986) Mathematical concepts in organic chemistry, Springer, Berlin Heidelberg New York
Cvetković D, Doob M, Sachs H (1980) Spectra of graphs — theory and application, Academic Press, New York
Heilbronner E (1962) Helv Chim Acta 45: 1722
Kiang YS, Chen ET (1983) Pure Appl Chem 55: 283
Hall GG (1977) Molec Phys 33: 551
Wild U, Keller J, Günthard HH (1969) Theor Chim Acta 14: 383
Wild U (1980) Theor Chim Acta 54: 245
Dias JR (1985) Nouv J Chim 9: 125
Gutman I, Kruszewski J (1985) Nouv J Chim 9: 669
Dias JR (1987) J Mol Struct (Theochem) 149: 213
Jiang YS, Chen GG (1990) Theor Chim Acta 76: 437
Gutman I (1983) J Chem Soc Faraday Trans II 79: 337
Hosoya H (1971) Bull Chem Soc Japan 44: 2332
Hosoya H, Hosoi K, Gutman I (1975) Theor Chim Acta 38: 37
Gutman I, Shalabi A (1984) Z. Naturforsch 39a: 107
Dias JR (1985) Theor Chim Acta 68: 107
Dias JR (1987) J Chem Educ 64: 213
Cioslowski J (1985) Z Naturforsch 40a: 1167
Hall GG (1986) Theor Chim Acta 70: 323
Kiang YS, Tang AC (1986) Int J Quantum Chem 29: 229
Jiang YS, Zhang HX (1989) Theor Chim Acta 75: 279
Marković S, Gutman I (1991) J Mol Struct (Theochem) 235: 81
Cyvin SJ, Gutman I (1988) Kekulé structures in benzenoid hydrocarbons (Lecture Notes in Chemistry 46), Springer, Berlin Heidelberg New York
Zhang FJ, Guo XF, Chen RS (1990) Topics Curr Chem 153: 181
He WC, He WJ (1990) Topics Curr Chem 153: 195
Sheng RQ (1990) Topics Curr Chem 153: 211
Hosoya H (1990) Topics Curr Chem 153: 273
El-Basil S (1990) Topics Curr Chem 153: 291
Gutman I, Cyvin SJ (1987) Chem Phys Letters 136: 137
Gutman I, Su LX, Cyvin SJ (1987) J Serb Chem Soc 52: 263
Cyvin SJ, Cyvin BN, Brunvoll J, Gutman I (1987) Z Naturforsch. 42a: 722
Bodroža O, Gutman I, Cyvin SJ, Tošić R (1988) J Math Chem 2: 287
Brunvoll J, Cyvin SJ, Cyvin BN, Gutman I, He WJ, He WC (1987) Math Chem 22: 105
He WC, He WJ, Cyvin BN, Cyvin SJ, Brunvoll J (1988) Math Chem 23: 201
Guo XF, Zhang FJ (1989) Math Chem 24: 85
Cyvin SJ, Cyvin BN, Brunvoll J (1990) J Math Chem 4: 47
Polansky OE, Gutman I (1980) Math Chem 8: 269
Cyvin BN, Brunvoll J, Cyvin SJ, Gutman I (1988) Math Chem 23: 163
Gutman I, Cyvin SJ (1988) Math Chem 23: 175
Gutman I, Cyvin SJ (1988) Chem Phys Letters 147: 121
Gutman I (1988) Graph Theory Notes NY 16: 26
Brunvoll J, Gutman I, Cyvin SJ (1989) Z Phys Chem (Leipzig) 270: 982
Hall GG (1988) Chem Phys Letters 145: 168
Gutman I, Cyvin SJ (1988) J Serb Chem Soc 53: 391
Hall GG, Dias JR (1989) J Math Chem 3: 233
Zhang FJ, Chen RS, Guo XF (1985) Graphs Comb 1: 383
Kostochka AV (1985) Proc 30 Int Wiss Koll TH Ilmenau F: 49
Zhang FJ, Chen RS (1987) Nature J 10: 163
Zhang FJ, Guo XF (1988) Math Chem 23: 229
Zhang FJ, Chen RS (1989) Acta Math Appl Sinica 1: 1
Sheng RQ (1989) Math Chem 24: 207
Gutman I, Cyvin SJ (1986) J Mol Struct (Theochem) 138: 325
Cyvin SJ, Gutman I (1987) J Mol Struct (Theochem) 150: 157
Cyvin SJ, Gutman I (1988) J Mol Struct (Theochem) 164: 183
Sheng RQ, Cyvin SJ, Gutman I (1989) J Mol Struct (Theochem) 187: 285
Sheng RQ (1987) Chem Phys Letters 142: 196
Guo XF, Zhang FJ (1990) J Math Chem 5: 157
Gutman I (1982) Math Chem 13: 173
Cyvin SJ (1986) Math Chem 20: 165
Chen RS, Cyvin SJ (1987) Math Chem 22: 175
John P (1990) private communication
Gutman I, Cioslowski J (1987) Publ Inst Math (Beograd) 42: 21
Balaban AT, Brunvoll J, Cyvin BN, Cyvin SJ (1988) Tetrahedron 44: 221
Zhang FJ, Chen RS, Guo XF, Gutman I (1986) J Serb Chem Soc 51: 537
Zhang FJ, Guo XF (1987) Math Chem 22: 181
El-Basil (1987) J Math Chem 1: 153
Hosoya H, Yamaguchi T (1975) Tetrahedron Letters: 4659
Gutman I, Hosoya H, Yamaguchi T, Motoyama A, Kuboi N (1977) Bull Soc Chim Beograd 42: 503
Ohkami N, Motoyama A, Yamaguchi T, Hosoya H, Gutman I (1981) Tetrahedron 37: 1113
Ohkami N, Hosoya H (1983) Theor Chim Acta 64: 153
Zhang FJ, Chen RS (1986) Math Chem 19: 179
He WJ, He WC (1986) Theor Chim Acta 70: 43
Ohkami N (1990) J Math Chem 5: 23
Gutman I (1982) Z Naturforsch 37a: 69
Gutman I, El-Basil S (1984) Z Naturforsch 39a: 276
Gutman I (1983) Wiss Z TH Ilmenau 29: 57
Zhang FJ, Chen RS (1989) Math Chem 24: 323
Zhang FJ, Chen RS (1991) Dicrete Appl Math 30: 63
John P (1989) Z Phys Chem (Leipzig) 270: 1023
He WC, He WJ (1990) Math Chem 25: 225
Cyvin SJ, Gutman I (1986) Z Naturforsch 41a: 1079
He WC, He WJ (1990) Math Chem 25: 237
Gutman I (1977) Theor Chim Acta 45: 309
El-Basil S (1984) Theor Chim Acta 65: 191
El-Basil S (1984) Theor Chim Acta 65: 199
El-Basil S (1986) J Chem Soc Faraday Trans II 82: 299
Gutman I, El-Basil S (1985) Z Naturforsch. 40a: 923
Gutman I, El-Basil S (1985) J Serb Chem Soc 50: 25
El-Basil S, Randić M (1988) J Chem Soc Faraday Trans II 84: 1875
Gutman I, Cyvin SJ (1989) Bull Chem Soc Japan 62: 1250
Gutman I, Teodorović AV, Kolaković N (1989) Z Naturforsch 44a: 1097
Chen ZB (1985) Chem Phys Letters 115: 291
Gutman I, Teodorović AV, Kolaković N (1990) J Serb Chem Soc 55: 363
Rouvray DH (1986) Sci Amer 255: 36
Balaban AT, Motoc I, Bonchev D, Mekenyan O (1983) Topics Curr Chem 114: 21
Hosoya H, Ohkami N (1986) J Comput Chem 4: 585
Gutman I (1988) Z Naturforsch 43a: 939
Randić M, Hosoya H, Polansky OE (1989) J Comput Chem 10: 683
Gutman I, Kolaković N (1990) Bull Serb Acad Sci 102: 39
Gutman I (1991) Rev Roum Chim, in press
Rouvray DH (1987) J Comput Chem 8: 478
Gutman I, Polansky OE (1986) Math Chem 20: 115
Polansky OE, Randić M, Hosoya H (1989) Math Chem 24: 3
Gutman I (1987) Chem Phys Letters 136: 134
Gutman I, Kennedy JW, Quintas LV (1990) Chem Phys Letters 173: 403
Gutman I, Marković S, Luković D, Radivojević V, Rančić S (1987) Coll Sci Papers Fac Sci Kragujevac 8: 15
Gutman I (1988) Publ Inst Math (Beograd) 43: 3
Gutman I, Rouvray DH (1990) Comput Chem 14: 29
Gutman I, Utvić D, Mukherjee AK (1991) J Serb Chem Soc 56: 59
Gutman I (1982) Bull Soc Chim Beograd 47: 453
Gutman I (1983) Croat Chem. Acta 56: 365
Gutman I, Babić D (1992) J Mol Struct (Theochem), in press
Sheng RQ (1991) Math Chem 26: 205
Zhang FJ, Chen RS, Guo XF, Gutman I (1991) Math Chem 26: 229
Cioslowski J (1991) J Math Chem 6: 111
Babić D (1992) J Math Chem, in press
Gutman I, Marković S, Grović V (1991) J Serb Chem Soc 56: 553
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© 1992 Springer-Verlag
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Gutman, I. (1992). Topological properties of benzenoid systems. In: Gutman, I. (eds) Advances in the Theory of Benzenoid Hydrocarbons II. Topics in Current Chemistry, vol 162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018561
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DOI: https://doi.org/10.1007/BFb0018561
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