Energies of unitary one-matching bi-Cayley graphs over finite commutative rings. (English) Zbl 1407.05121
Summary: Let \(R\) be a finite commutative ring with unit element \(1 \neq 0\), and let \(\mathcal{G}_R\) denote the unitary one-matching bi-Cayley graph over \(R\). In this paper, we determine the energies of \(\mathcal{G}_R\) and its line graph, respectively. We also characterize when \(\mathcal{G}_R\) as well as its line graph is hyperenergetic or hypoenergetic, respectively.
MSC:
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C76 | Graph operations (line graphs, products, etc.) |
Keywords:
unitary one-matching bi-Cayley graph; line graph; energy; hyperenergetic graph; hypoenergetic graphReferences:
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