Geodesic
The Petersen and Heawood graphs make up graphical twins via induced matchings
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 677-683

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Inspired by the Isaacs remark (published in 1975), we show that the Petersen and Heawood graphs (Pg and Hg) make up a bijectively linked pair of graphs. Another related new result is that Pg is uniquely decomposable into five induced 3-matchings. It shows a kind of the structural rigidity of Pg. Information on maximal matchings with sizes 3, 4 and 5 in Pg is recalled. Constructive proofs confirm that the strong chromatic index sq(Pg)=5 and sq(Hg)=7. The three numerical edge coloring partitions for Pg are also determined.
Keywords: Heawood graph, induced matchings, Petersen graph, strong chromatic index 
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Skupień, Zdzisław. The Petersen and Heawood graphs make up graphical twins via induced matchings. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 677-683. http://geodesic.mathdoc.fr/item/DMGT_2023_43_3_a5/