The Third Immanant of q-Laplacian Matrices of Trees and Laplacians of Regular Graphs

R. B. Bapat () and Sivaramakrishnan Sivasubramanian ()
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R. B. Bapat: Indian Statistical Institute, Delhi, Stat-Math Unit
Sivaramakrishnan Sivasubramanian: Indian Institute of Technology, Bombay, Department of Mathematics

A chapter in Combinatorial Matrix Theory and Generalized Inverses of Matrices, 2013, pp 33-40 from Springer

Abstract: Abstract Let A=(a i,j )1≤i,j≤n be an n×n matrix where n≥3. Let $\operatorname{det2}(A)$ and $\operatorname{det3}(A)$ be its second and third immanants corresponding to the partitions λ 2=2,1 n−2 and λ 3=3,1 n−3, respectively. We give explicit formulae for $\operatorname{det2}(A)$ and $\operatorname{det3}(A)$ when A is the q-analogue of the Laplacian of a tree T on n vertices and when A is the Laplacian of a connected r-regular graph G.

Keywords: Regular graphs; Laplacian matrices; Immanants of matrices; q-Analogue; 05C50 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1053-5_3

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DOI: 10.1007/978-81-322-1053-5_3

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