Laplacian coefficient, matching polynomial and incidence energy of trees with described maximum degree

Ya-Lei Jin, Yeong-Nan Yeh and Xiao-Dong Zhang ()
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Ya-Lei Jin: Shanghai Jiao Tong University
Yeong-Nan Yeh: Academia Sinica
Xiao-Dong Zhang: Shanghai Jiao Tong University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 3, No 25, 1345-1372

Abstract: Abstract Let $$\mathcal {L}(T,\lambda )=\sum _{k=0}^n (-1)^{k}c_{k}(T)\lambda ^{n-k}$$ L ( T , λ ) = ∑ k = 0 n ( - 1 ) k c k ( T ) λ n - k be the characteristic polynomial of its Laplacian matrix of a tree T. This paper studied some properties of the generating function of the coefficients sequence $$(c_0, \ldots , c_n)$$ ( c 0 , … , c n ) which are related with the matching polynomials of division tree of T. These results, in turn, are used to characterize all extremal trees having the minimum Laplacian coefficient generation function and the minimum incidence energy of trees with described maximum degree, respectively.

Keywords: Laplacian coefficient; Matching polynomial; Incidence energy; Tree; Subdivision tree; 05C25; 05C50 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-015-9977-4

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