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Locally finite self-interchange graphs


Authors: Benjamin L. Schwartz and Lowell W. Beineke
Journal: Proc. Amer. Math. Soc. 27 (1971), 8-12
MSC: Primary 05.40
DOI: https://doi.org/10.1090/S0002-9939-1971-0289349-5
MathSciNet review: 0289349
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Abstract: Graphs isomorphic to their interchanges are studied. Using prior results of more special cases, plus one new concept, it is possible to characterize all locally finite self-interchange graphs, finite and infinite, connected and disconnected, with loops and parallel edges admitted. All solutions are shown to be component-unions of graphs from six easily described classes.


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  • [1] A. Andreatta, Sui singrammi finiti commutati di altri, Inst. Lombardo Accad. Sci. Lett. Rend. A 98 (1964), 133-156. MR 31 #80. MR 0175804 (31:80)
  • [2] G. Chartrand, The existence of complete cycles in repeated line-graphs. Bull. Amer. Math. Soc. 71 (1965), 668-670. MR 31 #82. MR 0175806 (31:82)
  • [3] Capt. Bernard Clark, USMC, Private communication, 1964.
  • [4] Anna Maria Ghirlanda, Osservazioni sulle caratteristiche dei grafi o singrammi, Ann. Univ. Ferrara Sez. VII 11 (1962-65), 93-106. MR 32 #7446. MR 0190030 (32:7446)
  • [5] J. Krausz, Démonstration nouvelle d'une théorème de Whitney sur les réseaux, Mat. Fiz. Lapok 50 (1943), 75-85. (Hungarian) MR 8, 284. MR 0018403 (8:284h)
  • [6] Livio Porcu, Sui grafi autocommutati, Inst. Lombardo Accad. Sci. Lett. Rend. A 100 (1966), 665-677. MR 34 #7404. MR 0207589 (34:7404)
  • [7] V. Menon, The isomorphism betewen graphs and their adjoint graphs, Canad. Math. Bull. 8 (1965), 7-15. MR 30 #5299. MR 0175114 (30:5299)
  • [8] -, On repeated interchange graphs, Amer. Math Monthly 73 (1966), 986-989. MR 34 #2493. MR 0202631 (34:2493)
  • [9] -, Repeated adjoints of graphs, Proc. Internat. Sympos. Theory of Graphs (Rome, 1966), Gordon and Breach, New York; Dunod, Paris, 1967, pp. 245-248. MR 36 #6314. MR 0223266 (36:6314)
  • [10] L. Muracchini and A. Ghirlanda, Sul grafo commutato e sul grafo opposto di un grafo orientato, Atti. Sem. Mat. Fis. Univ. Modena 14 (1965), 87-97. MR 33 #2570. MR 0194360 (33:2570)
  • [11] Oystein Ore, Theory of graphs, Amer. Math. Soc. Colloq. Publ., vol. 38, Amer. Math. Soc., Providence, R. I., 1962. MR 27 #740. MR 0150753 (27:740)
  • [12] A. van Rooij and H. Wilf, The interchange graph of a finite graph, Acta. Math. Acad. Sci. Hungar. 16 (1965), 263-269. MR 33 #3959. MR 0195761 (33:3959)
  • [13] Gert Sabidussi, Existence and structure of self-adjoint graphs, Math. Z. 104 (1968), 257-280. MR 37 #2629. MR 0227044 (37:2629)
  • [14] B. L. Schwartz, On interchange graphs, Pacific J. Math. 27 (1968), 393-396. MR 38 #3174. MR 0234860 (38:3174)
  • [15] -, Infinite self-interchange graphs, Pacific J. Math. 31 (1969), 497-504. MR 0262107 (41:6717)
  • [16] -, Defining the interchange of a loop, Math. Mag. 43 (1970), 141-143. MR 1571864
  • [17] H. Whitney, Congruent graphs and the connectivity of graphs, Amer. J. Math. 54 (1932), 150-168. MR 1506881

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0289349-5
Keywords: Graph theory, interchange graphs
Article copyright: © Copyright 1971 American Mathematical Society

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