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The partial differential coefficients for the second weighted Bartholdi zeta function of a graph. (English) Zbl 1416.05094

Summary: We consider the second weighted Bartholdi zeta function of a graph \(G\), and present weighted versions for the results of D. Li and Y. Hou [ibid. 341, No. 3, 786–792 (2018; Zbl 1378.05038)] on the partial derivatives of the determinant part in the determinant expression of the Bartholdi zeta function of \(G\). Furthermore, we give a formula for the weighted Kirchhoff index of a regular covering of \(G\) in terms of that of \(G\).

MSC:

05C12 Distance in graphs
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
11M41 Other Dirichlet series and zeta functions

Citations:

Zbl 1378.05038
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Full Text: DOI

References:

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