On the permanental nullity and matching number of graphs

References

• Valiant LG. The complexity of computing the permanent. Theoret Comput Sci. 1979;8:189–201.
   Google Scholar
• Turner J. Generalized matrix functions and the graph isomorphism problem. SIAM J Appl Math. 1968;16:520–526.
   Web of Science ®Google Scholar
• Merris R, Rebman KR, Watkins W. Permanental polynomials of graphs. Linear Algebra Appl. 1981;38:273–288.
   Web of Science ®Google Scholar
• Kasum D, Trinajstić N, Gutman I. Chemical graph theory. III. On permanental polynomial. Croat Chem Acta. 1981;54:321–328.
   Web of Science ®Google Scholar
• Cash GG. The permanental polynomial. J Chem Inf Comput Sci. 2000;40:1203–1206.
   PubMedGoogle Scholar
• Belardo F, De Filippis V, Simić SK. Computing the permanental polynomial of a matrix from a combinatorial viewpoint. MATCH Commun Math Comput Chem. 2011;66:381–396.
   Web of Science ®Google Scholar
• Borowiecki M, Jóźwiak T. Computing the permanental polynomial of a multigraph. Discuss Math. 1982;5:9–16.
   Google Scholar
• Cash GG. Permanental polynomials of smaller fullerenes. J Chem Inf Comput Sci. 2000;40:1207–1209.
   PubMedGoogle Scholar
• Chen R. A note on the relations between the permanental and characteristic polynomials of coronoid hydrocarbons. MATCH Commun Math Comput Chem. 2004;51:137–148.
   Google Scholar
• Geelen J. An algebraic approach to matching problems. RIMS Kokyuroku. 2001;1185:63–71.
   Google Scholar
• Gutman I. Permanents of adjacency matrices and their dependence on molecular structures. Polycycl Aromat Comp. 1998;12:281–287.
   Web of Science ®Google Scholar
• Gutman I, Cash GG. Relations between the permanental and characteristic polynomials of fullerenes and benzenoid hydrocarbons. MATCH Commun Math Comput Chem. 2002;45:55–70.
   Google Scholar
• Huo Y, Liang H, Bai F. An efficient algorithm for computing permanental polynomials of graphs. Comput Phys Commun. 2006;175:196–203.
   Web of Science ®Google Scholar
• Wu T, Zhang H. Some analytical properties of the permanental polynomial of a graph. Ars Combin. 2015;123:261–267.
   Web of Science ®Google Scholar
• Yan W, Zhang F. On the permanental polynomial of some graphs. J Math Chem. 2004;35:175–188.
   Web of Science ®Google Scholar
• Zhang H, Li W. Computing the permanental polynomials of bipartite graphs by Pfaffian orientation. Discrete Appl Math. 2012;160:2069–2074.
   Web of Science ®Google Scholar
• Cvetković D, Doob M, Sachs H. Spectra of graphs. New York (NY): Academic Press; 1980.
   Google Scholar
• Brenner JL, Brualdi RA. Eigenschaften der permanentefunktion [Properties of the permanent function]. Arch Math. 1967;18:585–586.
   Web of Science ®Google Scholar
• Merris R. Two problems involving Schur functions. Linear Algebra Appl. 1975;10:155–162.
   Web of Science ®Google Scholar
• Borowiecki M. On spectrum and per-spectrum of graphs. Publ Inst Math. 1985;38:31–33.
   Google Scholar
• Zhang H, Liu S, Li W. A note on the permanental roots of bipartite graphs. Disscuss Math Graph Theory. 2014;34:49–56.
   Web of Science ®Google Scholar
• Liu S, Zhang H. On the characterizing properties of the permanental polynomials of graphs. Linear Algebra Appl. 2013;438:157–172.
   Web of Science ®Google Scholar
• Liu S, Zhang H. Characterizing properties of permanental polynomials of lollipop graphs. Linear Multi Algebra. 2014;62:419–444.
   Web of Science ®Google Scholar
• Wu T, Zhang H. Per-spectral and adjacency spectral characterizations of a complete graph removing six edges. Discrete Appl Math. 2016;203:158–170.
   Web of Science ®Google Scholar
• Zhang H, Wu T, Lai H. Per-spectral characterizations of some edge-deleted subgraphs of a complete graph. Linear Multi Algebra. 2015;63:397–410.
   Web of Science ®Google Scholar
• Wu T, Zhang H. Per-spectral characterizations of graphs with extremal per-nullity. Linear Algebra Appl. 2015;484:13–26.
   Web of Science ®Google Scholar
• Lovász L, Plummer MD. Matching theory. New York (NY): American Mathematical Society; 2009.
   Google Scholar
• Yu Q, Liu G. Graph factors and matching extensions. Beijing: Springer; 2009.
   Google Scholar
• Chartrand G, Polimeni AD, Stewart MJ. The existance of 1-factors in line graphs, squares and total graphs. Indag Math. 1973;35:228–232.
   Google Scholar