Nuciferous Graph
المؤلف:
Ghorbani, E
المصدر:
"Nontrivial Nuciferous Graphs Exist." 18 Mar 2016. http://arxiv.org/pdf/1603.03741.pdf.
الجزء والصفحة:
...
14-4-2022
1280
Nuciferous Graph
Let 
be a simple graph with nonsingular (0,1) adjacency matrix 
. If all the diagonal entries of the matrix inverse 
are zero and all the off-diagonal entries of 
are nonzero, then 
is called a nuciferous graph (Ghorbani 2016).
The path graph 
has adjacency matrix (and adjacency matrix inverse) given by
which is therefore nuciferous. Initially, this was the only example known, and in fact, no others exist on 10 or fewer nodes (E. Weisstein, Mar. 18, 2016). As a result, it was conjectured by Sciriha et al. (2013) that no others exist.
This conjecture was disproved by Ghorbani (2016) who found 21 Cayley graphs examples on 24, 28, and 30 nodes.
REFERENCES
Ghorbani, E. "Nontrivial Nuciferous Graphs Exist." 18 Mar 2016. http://arxiv.org/pdf/1603.03741.pdf.
Fowler, P. W.; Pickup, B. T.; Todorova, T. Z.; de los Reyes, R.; and Sciriha, I. "Omni-Conducting Fullerenes." Chem. Phys. Lett., 568-569, 33-35, 2013.
Sciriha, I. "Molecular Graphs with Analogous Conducting Connections." The 4th Biennial Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM). St. John's, Newfoundland: Memorial University of Newfoundland, 2013.
Sciriha, I.; Debono, M.; Borg, M.; Fowler, P.; and Pickup, B. T. "Interlacing-Extremal Graphs." Ars Math. Contemp. 6, 261-278, 2013.
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