Gutman–Vidović's maximal-energy conjecture for bicyclic molecular graphs

Let Pn6,6P_n^{6,6} denote the bicyclic molecular graph of order nn corresponding to the alpha,beta diphenyl-polyene C6H5(CH)n12C6H5C_6H_5(CH)_{n-12}C_6H_5. Gutman–Vidović's conjecture. For n=14n=14 and n16n\geq 16, the bicyclic molecular graph of order nn with maximal energy is Pn6,6P_n^{6,6}. The source explains that the conjecture was completely solved for bipartite bicyclic graphs, while it remained open for non-bipartite bicyclic graphs at the point discussed.

Sources & referencesView supporting material

Primary source

Xueliang Li, Yongtang Shi, Meiqin Wei and Jing Li, “On a conjecture about tricyclic graphs with maximal energy”, arXiv:1312.0204 (2014).

Additional references

2 papers in this index state this conjecture (2011–2013). The statement above is taken from the most recent of them; the others are arXiv:1101.0058.

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