Geodesic
Classification of cubic tricirculant nut graphs
Ivan Damnjanović1 ; Nino Bašić2 ; Tomaž Pisanski2 ; Arjana Žitnik3
1University of Niš, Faculty of Electronic Engineering
2University of Primorska
3University of Ljubljana
The electronic journal of combinatorics, Tome 31 (2024) no. 2
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A nut graph is a simple graph whose adjacency matrix has the eigenvalue zero with multiplicity one such that its corresponding eigenvector has no zero entries. It is known that there exist no cubic circulant nut graphs. A bicirculant (resp. tricirculant) graph is defined as a graph that admits a cyclic group of automorphisms having two (resp. three) orbits of vertices of equal size. We show that there exist no cubic bicirculant nut graphs and we provide a full classification of cubic tricirculant nut graphs.
DOI : 10.37236/12668
Classification : 05C50, 11C08, 12D05
Mots-clés : circulant nut graphs of given degree

Ivan Damnjanović  1   ; Nino Bašić  2   ; Tomaž Pisanski  2   ; Arjana Žitnik  3

1 University of Niš, Faculty of Electronic Engineering
2 University of Primorska
3 University of Ljubljana 
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     title = {Classification of cubic tricirculant nut graphs},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
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     doi = {10.37236/12668},
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Ivan Damnjanović; Nino Bašić; Tomaž Pisanski; Arjana Žitnik. Classification of cubic tricirculant nut graphs. The electronic journal of combinatorics, Tome 31 (2024) no. 2. doi: 10.37236/12668

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