A matrix-weighted zeta function of a graph. (English) Zbl 1286.05100
Summary: We define a matrix-weighted \(L\)-function of a graph \(G\), and give a determinant expression of it. As a corollary, we present a decomposition formula for the matrix-weighted zeta function of a regular covering of \(G\) by a product of matrix-weighted \(L\)-functions of \(G\).
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
| 11M99 | Zeta and \(L\)-functions: analytic theory |
References:
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