On the number of spanning trees in alternating polycyclic chains

On the number of spanning trees in alternating polycyclic chains J Math Chem https://doi.org/10.1007/s10910-018-0918-1 ORIGINAL PAPER On the number of spanning trees in alternating polycyclic chains Tomislav Došlic ´ Received: 21 June 2017 / Accepted: 21 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract In this paper we generalize and unify results of several recent papers by presenting explicit formulas for the number of spanning trees in a class of unbranched polycyclic polymers. From these formulas we immediately deduce the asymptotic behavior of the number of spanning trees, and, as a consequence, we obtain combina- torial proofs of some identities for Chebyshev polynomials of the second kind. Keywords Number of spanning trees · Complexity of a graph · Chebyshev polynomials of the second kind · Polycyclic chain 1 Introduction The number of spanning trees τ(G) of a graph G, also known as the complexity of G, is a well known and well researched graph-theoretical invariant. There is a wealth of results for various special cases—some hundred and seventy integer sequences enumerating spanning trees in various classes of graphs are listed in [6]; probably n−2 the best known is the celebrated Cayley formula τ(K ) = n [4]. The number of spanning trees is also http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Chemistry Springer Journals

On the number of spanning trees in alternating polycyclic chains

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Chemistry; Physical Chemistry; Theoretical and Computational Chemistry; Math. Applications in Chemistry
ISSN
0259-9791
eISSN
1572-8897
D.O.I.
10.1007/s10910-018-0918-1
Publisher site
See Article on Publisher Site

Abstract

J Math Chem https://doi.org/10.1007/s10910-018-0918-1 ORIGINAL PAPER On the number of spanning trees in alternating polycyclic chains Tomislav Došlic ´ Received: 21 June 2017 / Accepted: 21 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract In this paper we generalize and unify results of several recent papers by presenting explicit formulas for the number of spanning trees in a class of unbranched polycyclic polymers. From these formulas we immediately deduce the asymptotic behavior of the number of spanning trees, and, as a consequence, we obtain combina- torial proofs of some identities for Chebyshev polynomials of the second kind. Keywords Number of spanning trees · Complexity of a graph · Chebyshev polynomials of the second kind · Polycyclic chain 1 Introduction The number of spanning trees τ(G) of a graph G, also known as the complexity of G, is a well known and well researched graph-theoretical invariant. There is a wealth of results for various special cases—some hundred and seventy integer sequences enumerating spanning trees in various classes of graphs are listed in [6]; probably n−2 the best known is the celebrated Cayley formula τ(K ) = n [4]. The number of spanning trees is also

Journal

Journal of Mathematical ChemistrySpringer Journals

Published: May 30, 2018

References

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