Interlace polynomials of lollipop and tadpole graphs

Christina L Eubanks-Turner, Kathryn Cole, Megan Lee


In this paper, we examine interlace polynomials of lollipop and

tadpole graphs. The lollipop and tadpole graphs are similar in that they both

include a path attached to a graph by a single vertex. In this paper we give

both explicit and recursive formulas for each graph, which extends the work of

Arratia, Bollobas and Sorkin, among others. We also give special values,

examine adjacency matrices and behavior of coecients of these polynomials.


graph polynomial, interlace polynomial, lollipop graph

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A. Ali, H. Abdullah, and G. Saleh, Hosoya polynomials and Wiener indices of carbon nanotubes using mathematica programming, Journal of Discrete Mathematical Sciences and Cryptography, (2021), 1-12, article in press.

J. Almeida, Interlace Polynomials of Cycles with One Additional Chord, Theses, Dissertations and Culminating Projects (2018).

C. Anderson, J. Cutler, A.J. Radcliffe, and L. Traldi, On the interlace polynomials of forests. Discrete Mathematics 310 (1) (2010), 31–36.

R. Arratia, B. Bollóbas, D. Coppersmith, and G. Sorkin, Euler Circuits and DNA sequencing by hybridization, Discrete Applied Mathematics 104 (2000), 63–96.

R. Arratia, B. Bollóbas, and G. Sorkin, The interlace polynomial of a graph, Journal of Combinatorial Theory, 92 (2004), 199–233.

J. Awan and O. Bernardi, Tutte polynomials for directed graphs, Journal of Combinatorial Theory, Series B, 140 (2020), 192–247.

P. Balister, B. Bollóbas, J. Cutler, and L. Pebody, The interlace polynomial of Graphs at -1, Europ. J. Combinatorics 23 (2002), 761–767.

A. Bouchet, Graph polynomials derived from Tutte Martin Polynomials, Discrete Mathematics 302 (2005), 32–38.

F. Chaudhry, M. Husin, F. Afzal, D. Afzal, M. Ehsan, M. Cancan, and M. Farahani, M-polynomials and degree-based topological indices of tadpole graph, Journal of Discrete Mathematical Sciences and Cryptography 24 (7) (2021), 2059–2072.

H. Chen and Q. Guo, Tutte polynomials of alternating polycyclic chains, J Math Chem 57 (2019), 2248–2260.

C. Eubanks-Turner, A. Li, Interlace polynomials of friendship graphs, Electronic Journal of Graph Theory and Applications 6 (2) (2018), 269–281.

M. Ghorbani, M. Dehmer, S. Cao, L. Feng, J. Tao, F. Emmert-Streib, On the zeros of the partial Hosoya polynomial of graphs, Information Sciences 524 (2020), 199–215.

A. Li and Q. Wu, Interlace polynomial of ladder graphs, Journal of Combinatorics, Information & System Sciences 35 (2010), 261–273.

H. Lin, L. Zhang, and J. Xue, Majorization, degree sequence and Aα-spectral characterization of graphs, Discrete Mathematics 343 (12) (2020), 112–132.

Y. Liu, T. Tan, and M. Yoshinaga, G-Tutte polynomials and abelian lie group arrangements, International Mathematics Research Notices 1 (2) (2021), 150–188.

S. Nomani and A. Li, Interlace polynomials of n-claw graphs, Journal of Combinatorics and Combinatorial Computing 88 (2014), 111–122.

A. Seeger and D. Sossa, Extremal problems involving the two largest complementarity eigenvalues of a graph, Graphs and Combinatorics 36 (2020), 1–25.

L. Traldi, On the interlace polynomials, Journal of Combinatorial Theory, Series B, 103 (2013), 184–208.

Y. Zhang, L. Xiaogang, B. Zhang, and Y. Xuerong, The lollipop graph is determined by its Q-spectrum, Discrete Mathematics 309 (2009), 3364–3369.


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