Geodesic
On generalizations of the Petersen graph and the Coxeter graph
Marko Orel1
11) University of Primorska, FAMNIT, Glagoljaška 8, 6000 Koper, Slovenia 2) IMFM, Jadranska 19, 1000 Ljubljana, Slovenia 3) University of Primorska, IAM, Muzejski trg 2, 6000 Koper, Slovenia
The electronic journal of combinatorics, Tome 22 (2015) no. 4
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In this note we consider two related infinite families of graphs, which generalize the Petersen and the Coxeter graph. The main result proves that these graphs are cores. It is determined which of these graphs are vertex/edge/arc-transitive or distance-regular. Girths and odd girths are computed. A problem on hamiltonicity is posed.A Corrigendum for this paper was added on August 19, 2017.
DOI : 10.37236/3759
Classification : 05C50, 15B33, 15B57
Mots-clés : core, Petersen graph, Coxeter graph, Hermitian matrix, symmetric matrix

Marko Orel  1

1 1) University of Primorska, FAMNIT, Glagoljaška 8, 6000 Koper, Slovenia 2) IMFM, Jadranska 19, 1000 Ljubljana, Slovenia 3) University of Primorska, IAM, Muzejski trg 2, 6000 Koper, Slovenia 
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     author = {Marko Orel},
     title = {On generalizations of the {Petersen} graph and the {Coxeter} graph},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {4},
     doi = {10.37236/3759},
     zbl = {1327.05217},
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Marko Orel. On generalizations of the Petersen graph and the Coxeter graph. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/3759

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