Liu–Shan–Xu conjecture on the maximum edge Mostar index of bicyclic graphs
Liu–Shan–Xu conjecture on the maximum edge Mostar index of bicyclic graphs
Let be the size of a bicyclic graph, and let and denote the bicyclic graphs shown in the source's Figures X and Y, respectively. Liu–Shan–Xu's conjecture. If is sufficiently large, then and have the maximum edge Mostar index among bicyclic graphs of size . 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.
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Primary source
Fazal Hayat, Shou-Jun Xu and Bo Zhou, “Disproof of a conjecture on the edge Mostar index”, arXiv:2306.02761 (2024).
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