A bibliography of graph equations

Graph equations are equations in which the unknowns are graphs. Many problems and results in graph theory can be formulated in terms of graph equations. Here we offer a classification and a large bibliography of graph equations.

[1]  Frank Harary.  A Characterization of Block-Graphs , 1963, Canadian Mathematical Bulletin.

[2]  Fred S. Roberts,et al.  A Characterization of Clique Graphs. , 1971 .

[3]  T Rojano,et al.  Characterization of n-path graphs and of graphs having nth root , 1974 .

[4]  Lowell W. Beineke,et al.  Derived graphs with derived complements , 1971 .

[5]  Robert L. Hemminger,et al.  Line isomorphisms on dipseudographs , 1973 .

[6]  Michael F. Capobianco,et al.  Tournaments and Tensor Products of Digraphs , 1967 .

[7]  Michael F. Capobianco.  Some Theorems on Tensor Composite Graphs , 1970 .

[8]  Frank Harary,et al.  Graph Theory , 2016 .

[9]  Jacobus H. van Lint,et al.  Directed graphs with unique paths of fixed length , 1978, J. Comb. Theory, Ser. B.

[10]  V. V. Menon.  On Repeated Interchange Graphs , 1966 .

[11]  Martin Aigner,et al.  Graphs whose complement and line graph are isomorphic , 1969 .

[12]  M. Behzad.  A CHARACTERIZATION OF TOTAL GRAPHS , 1970 .

[13]  J. M. S. Simoes Pereira.  Corrigendum: “On the Boolean Matrix Equation M ′ =∨ i=1 M i ” , 1967 .

[14]  S. Hedetniemi,et al.  Line graphs of triangleless graphs and iterated clique graphs , 1972 .

[15]  K. B. Reid,et al.  Connectivity in Products of Graphs , 1970 .

[16]  A. Hoffman.  On the Polynomial of a Graph , 1963 .

[17]  Robert L. Hemminger,et al.  Infinite digraphs isomorphic with their line digraphs , 1976, J. Comb. Theory, Ser. B.

[18]  H. Whitney.  Congruent Graphs and the Connectivity of Graphs , 1932 .

[19]  László Lovász,et al.  On the cancellation law among finite relational structures , 1971 .

[20]  Herbert S. Wilf,et al.  The interchange graph of a finite graph , 1965 .

[21]  Jean-Claude Bermond,et al.  Graphe représentaif des arêtes d'un multigraphe , 1973 .

[22]  J. M. S. Simões-Pereira,et al.  Just two total graphs are complementary , 1976 .

[23]  Ralph McKenzie,et al.  Cardinal multiplication of structures with a reflexive relation , 1971 .

[24]  R. Z. Norman,et al.  Some properties of line digraphs , 1960 .

[25]  E. Sampathkumar.  On tensor product graphs , 1975 .

[26]  J. M. S. Simoes Pereira.  On the Boolean Matrix Equation M ′ =∨ i=1 M i , 1965 .

[27]  Clement W. H. Lam,et al.  On Some Solutions of Ak = dl + lambda J , 1977, J. Comb. Theory, Ser. A.

[28]  N. S. Mendelsohn,et al.  Gaps in the exponent set of primitive matrices , 1964 .

[29]  Robert L. Hemminger.  Isomorphism-induced line isomorphisms on pseudographs , 1971 .

[30]  Benjamin L. Schwartz.  On interchange graphs , 1968 .

[31]  Heydar Radjavi,et al.  Structure of Regular Total Graphs , 1969 .

[32]  F. Escalante.  Über iterierte Clique-Graphen , 1973 .

[33]  V. V. Menon.  The Isomorphism between Graphs and their Adjoint Graphs , 1965, Canadian Mathematical Bulletin.

[34]  Heydar Radjavi,et al.  THE TOTAL GROUP OF A GRAPH , 1968 .

[35]  V. V Menon.  On repeated interchange graphs. II , 1971 .

[36]  M. Aigner.  On the linegraph of a directed graph , 1967 .

[37]  David Burns,et al.  Every (p, p-2) graph is contained in its complement , 1977, J. Graph Theory.

[38]  Willibald Dörfler,et al.  Das lexikographische Produkt gerichteter Graphen , 1972 .

[39]  Benjamin L. Schwartz,et al.  INFINITE SELF-INTERCHANGE GRAPHS , 1969 .

[40]  Michael Capobianco,et al.  On Characterizing Tensor Composite Graphs , 1970 .

[41]  D. Knuth.  Notes on central groupoids , 1970 .

[42]  Donald J. Miller.  The Categorical Product of Graphs , 1968, Canadian Journal of Mathematics.

[43]  Lowell W. Beineke,et al.  Locally finite self-interchange graphs , 1971 .

[44]  A. Mukhopadhyay.  The square root of a graph , 1967 .

[45]  Wilfried Imrich,et al.  Über das lexikographische Produkt von Graphen , 1969 .

[46]  Dragos M. Cvetkovi,et al.  Graph equations for line graphs and total graphs , 1975 .

[47]  Alan J. Hoffman,et al.  On Moore Graphs with Diameters 2 and 3 , 1960, IBM J. Res. Dev..

[48]  Michael Capobianco,et al.  Tensor products of digraphs and the structure of groups of pairs , 1969 .

[49]  Wilfried Imrich.  On products of graphs and regular groups , 1972 .

[50]  R. Hamelink.  A partial characterization of clique graphs , 1968 .

[51]  L. Beineke.  Characterizations of derived graphs , 1970 .