Geodesic
A vertex-weighted Tutte symmetric function, and constructing graphs with equal chromatic symmetric function
José Aliste-Prieto1 ; Logan Crew2 ; Sophie Spirkl2 ; José Zamora1
1Universidad Andres Bello
2University of Waterloo
The electronic journal of combinatorics, Tome 28 (2021) no. 2
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This paper has two main parts. First, we consider the Tutte symmetric function XB, a generalization of the chromatic symmetric function. We introduce a vertex-weighted version of XB and show that this function admits a deletion-contraction relation. We also demonstrate that the vertex-weighted XB admits spanning-tree and spanning-forest expansions generalizing those of the Tutte polynomial by connecting XB to other graph functions. Second, we give several methods for constructing nonisomorphic graphs with equal chromatic and Tutte symmetric functions, and use them to provide specific examples.
DOI : 10.37236/10018
Classification : 05E05, 05C31
Mots-clés : Tutte polynomial, \(V\)-polynomial

José Aliste-Prieto  1   ; Logan Crew  2   ; Sophie Spirkl  2   ; José Zamora  1

1 Universidad Andres Bello
2 University of Waterloo 
@article{10_37236_10018,
     author = {Jos\'e Aliste-Prieto and Logan Crew and Sophie Spirkl and Jos\'e Zamora},
     title = {A vertex-weighted {Tutte} symmetric function, and constructing graphs with equal chromatic symmetric function},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {2},
     doi = {10.37236/10018},
     zbl = {1461.05236},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10018/}
}
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José Aliste-Prieto; Logan Crew; Sophie Spirkl; José Zamora. A vertex-weighted Tutte symmetric function, and constructing graphs with equal chromatic symmetric function. The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/10018

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