Chen–Wang conjecture on independence polynomials of clique-corona graphs

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Let Kt,nK_{t,n} be the complete bipartite graph with parts of sizes tt and nn, and let Kt,n∘K1K_{t,n}\circ K_1 denote its corona with K1K_1. Write I(G;x)I(G;x) for the independence polynomial of a graph GG. Chen–Wang conjecture. For every tt, the polynomial I(Kt,n∘K1;x)I(K_{t,n}\circ K_1;x) is log-concave and therefore unimodal. The conjecture was proposed after the corresponding calculation for K2,n∘K1K_{2,n}\circ K_1; the supplied text gives no resolution status.

References

Primary source

Bao-Xuan Zhu, “Operations of graphs and unimodality of independence polynomials”, arXiv:1309.7673 (2013).

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