Geodesic
On graphs having no flow roots in the interval \((1,2)\)
F.M. Dong1
1Nanyang Technological University
The electronic journal of combinatorics, Tome 22 (2015) no. 1
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For any graph $G$, let $W(G)$ be the set of vertices in $G$ of degrees larger than 3. We show that for any bridgeless graph $G$, if $W(G)$ is dominated by some component of $G - W(G)$, then $F(G,\lambda)$ has no roots in the interval (1,2), where $F(G,\lambda)$ is the flow polynomial of $G$. This result generalizes the known result that $F(G,\lambda)$ has no roots in (1,2) whenever $|W(G)| \leq 2$. We also give some constructions to generate graphs whose flow polynomials have no roots in $(1,2)$.
DOI : 10.37236/3841
Classification : 05C31, 05C15, 05C25
Mots-clés : chromatic polynomial, flow polynomial

F.M. Dong  1

1 Nanyang Technological University 
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     author = {F.M. Dong},
     title = {On graphs having no flow roots in the interval \((1,2)\)},
     journal = {The electronic journal of combinatorics},
     year = {2015},
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F.M. Dong. On graphs having no flow roots in the interval \((1,2)\). The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/3841

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