Geodesic
Chromatic roots of a ring of four cliques
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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For any positive integers $a,b,c,d$, let $R_{a,b,c,d}$ be the graph obtained from the complete graphs $K_a, K_b, K_c$ and $K_d$ by adding edges joining every vertex in $K_a$ and $K_c$ to every vertex in $K_b$ and $K_d$. This paper shows that for arbitrary positive integers $a,b,c$ and $d$, every root of the chromatic polynomial of $R_{a,b,c,d}$ is either a real number or a non-real number with its real part equal to $(a+b+c+d-1)/2$.
DOI : 10.37236/638
Classification : 05C15, 05C31, 11C08, 65H04
Mots-clés : graph, chromatic polynomial, chromatic root, ring of cliques 
@article{10_37236_638,
     author = {F. M. Dong and Gordon Royle and Dave Wagner},
     title = {Chromatic roots of a ring of four cliques},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/638},
     zbl = {1222.05054},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/638/}
}
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F. M. Dong; Gordon Royle; Dave Wagner. Chromatic roots of a ring of four cliques. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/638

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