Liu–Shan–Xu conjecture on the maximum edge Mostar index of bicyclic graphs

Let mm be the size of a bicyclic graph, and let BmB_m and Bm5B^5_m denote the bicyclic graphs shown in the source's Figures X and Y, respectively. Liu–Shan–Xu's conjecture. If mm is sufficiently large, then BmB_m and Bm5B^5_m have the maximum edge Mostar index among bicyclic graphs of size mm. The conjecture concerns the extremal edge Mostar index among bicyclic graphs. The source paper disproves it by determining the unique graph maximizing the edge Mostar index for bicyclic graphs with fixed size.

Sources & referencesView supporting material

Primary source

Fazal Hayat, Shou-Jun Xu and Bo Zhou, “Disproof of a conjecture on the edge Mostar index”, arXiv:2306.02761 (2024).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.