Graph symmetry and eigensolutions: A brief review

Trinajstić, 1992 Dias, 1993 McClelland, 1974, Graphical method for factorizing secular determinants of Hückel molecular orbital theory, J. Chem. Soc. Faraday. Trans., 2, 1453, 10.1039/F29747001453 McClelland, 1982, Eigenvalues of the topological matrix splitting of graphs with symmetrical components and alternant graphs, J. Chem. Soc. Faraday. Trans., 2, 911, 10.1039/f29827800911 McClelland, 1982, On the graphical factorization of Hückel characteristic equations, Mol. Phys., 45, 189, 10.1080/00268978200100151 Hall, 1977, On the eigenvalues of molecular graphs, Mol. Phys., 33, 551, 10.1080/00268977700100471 Hall, 1957, The bond orders of some conjugated hydrocarbon molecules, Trans. Faraday Soc., 53, 573, 10.1039/tf9575300573 D'Amato, 1979, Eigenvalues of graphs with twofold symmetry, Mol. Phys., 37, 1363, 10.1080/00268977900101001 D'Amato, 1979, Eigenvalues of graphs with threefold symmetry, Theor. Chim. Acta, 53, 319, 10.1007/BF00555691 D'Amato, 1979, Isospectral and subspectral molecules, Croat. Chem. Acta, 54, 1 Dias, 1988, Characteristic polynomials and eigenvalues of molecular graphs with a greater that two fold axis of symmetry, J. Mol. Struct., 165, 125, 10.1016/0166-1280(88)87011-8 Davidson, 1981, Spectral analysis of graphs by cyclic automorphism subgroups, Theor. Chim. Acta, 58, 193, 10.1007/BF00551119 Shen, 1990, Splitting of N-fold rotationally symmetric graphs, Int. J. Quant. Chem., 38, 351, 10.1002/qua.560380405 Hosoya, 1994, Efficient way for factorizing the characteristic polynomial of highly symmetrical graphs such as the buckminsterfullerene, Fullerene Sci. Technol., 2, 381, 10.1080/15363839408010475 Hosoya, 2004, Supersymmetry of hexabenzocoronene torus, Croat. Chem. Acta, 77, 89 Gutman, 1986 Gutman, 1981, Topological studies on heteroconjugated molecules. III. On the law of alternating polarity, Z. Naturforsch., 36a, 1112, 10.1515/zna-1981-1016 Gutman, 1983, A new pairing theorem, Z. Naturforsch., 39a, 152 Mukherjee, 1993, Graph factorization: a new mode of application of a vertex-alternation scheme, Int. J. Quant. Chem., 46, 519, 10.1002/qua.560460403 Mukherjee, 2000, Characteristic polynomials of linear polyacenes and their subspectrality, Proc. Indian Acad. Sci., 112, 27, 10.1007/BF02704297 Fowler, 1991, The higher fullerenes: a candidate for the structure of C78, J. Chem. Soc. Faraday. Trans., 87, 3103, 10.1039/ft9918703103 Datta, 1999, Strongly subspectral pairs in C50+10n and C60+12n fullerenes via a common generic graph, Phys. Chem. Chem. Phys., 1, 2919, 10.1039/a902553g Shen, 1990, A representation of the McClelland method of graph splitting. Stack graphs, Int. J. Quant. Chem., 37, 113, 10.1002/qua.560370202 Klein, 1990, Graphical and color-pairing symmetries, Int. J. Quant. Chem., 37, 423, 10.1002/qua.560370413 Ghosh, 2014, Analytical eigenspectra of alternant edge-weighted graphs of linear chains and cycles: some applications, Mol. Phys., 112, 2093, 10.1080/00268976.2014.886737 Ghosh, 2014, Eigensolutions of dodecahedron graphs, Chem. Phys. Lett., 594, 41, 10.1016/j.cplett.2014.01.020 Ghosh, 2011, Use of symmetry plane fragmentation and graph squaring techniques to express the eigenspectra for some vertex-weighted graphs of linear chains and cycles in analytical form, Mol. Phys., 109, 267, 10.1080/00268976.2010.520039 Mandal, 2008, Eigenspectral analysis of pendant vertex- and pendant edge-weighted graphs of linear chains, cycles, and stars, Bull. Chem. Soc. Jpn., 81, 956, 10.1246/bcsj.81.956 Mandal, 2005, Use of symmetry plane and subsequent subtraction for obtaining eigenspectra of some complicated graphs in analytical forms, J. Mol. Struct., 757, 99, 10.1016/j.theochem.2005.08.011 Mandal, 2005, Construction and utilisation of planar graphs of two series of IPR fullerenes through the use of threefold rotational symmetry, Int. J. Quant. Chem., 105, 201, 10.1002/qua.20693 Mandal, 2005, Graph theoretical procedure for obtaining analytical expressions of eigenspectra of linear chains and cycles with alternant vertex weights and same edge weight: application to some complicated graphs, Int. J. Quant. Chem., 103, 140, 10.1002/qua.20503 Mandal, 2004, Construction of planar graphs for IPR fullerenes using5- and 6-fold rotational symmetry: some eigenspectral analysis, Phys. Chem. Chem. Phys., 6, 2040, 10.1039/b316775e Klein, 2015, Local symmetries for molecular graphs, MATCH, Commun. Math. Comput. Chem., 74, 247 Hückel, 1931, Quantentheoretische beitrgge zum benzolproblem, Die Elekfronenkonfigurafion des Benzols und verwandfer Verbindungen, 70, 204 Hückel, 1932, Quantentheoretische Beitr∼ge zum Problem der aromatischen und unges∼ttigten Verbindungen, HI, 76, 628 Coulson, 1940, Note on the method of molecular orbitals, Proc. Camb. Phil. Soc., 36, 193, 10.1017/S0305004100017163 Rutherford, 1946, Some continuant determinants arising in physics and chemistry, Proc. R. Soc. Edinb., A62, 229 Coulson, 1950, Notes on the secular determinant in molecular orbital theory, Proc. Camb. Phil. Soc., 46, 202, 10.1017/S0305004100025639 Coulson, 1965 Gunthard, 1956, Zusammenhang von Graphentheorie und MO-Theorie von MolekelnmitSystemenkonjugierterBindungen, Helv. Chim. Acta, 39, 1645, 10.1002/hlca.19560390623 Schmidtke, 1966, LCAO description of symmetric molecules by unified theory of finite graphs, J. Chem. Phys., 45, 3920, 10.1063/1.1727439 Streitwieser, 1961 Cvetković, 1979 1976 Karmakar, 2015, Eigensolutions of cyclopolyacene graphs, Mol. Phys., 113, 719, 10.1080/00268976.2014.971898 Karmakar, 2019, {X,Y}-cyclacene graphs with next nearest neighbor interactions, Polycycl. Aromat. Comp., 39, 159, 10.1080/10406638.2017.1293699 Glass, 1975, Combinatorial and topological methods in nonlinear chemical kinetics, J. Chem. Phys., 63, 1325, 10.1063/1.431518