Owing to its unique characteristics, graphene is inherently susceptible to instabilities that can give rise to novel ordered phases. One representative example is the bond-density wave, which leads to Kekulé-distorted structure with alternating bond lengths, accompanied by modified electronic and phononic properties. Here, an effective distance-dependent framework is presented to analyze the associated coupling behavior between the electron and phonon degrees of freedom. Within this approach, the strength of the bond-resolved electron-phonon interaction is found to scale linearly with the electronic hopping, contributing to a uniform picture of this relationship in distorted graphene. The analysis also reveals that the Kekulé order induces a pronounced anisotropy in the coupling, leading to its nonuniform variation under bond-length modulation. These results provide microscopic insight into the electron-phonon interaction in Kekulé-ordered graphene, and suggest a potential route to tune this coupling and related properties through controlled spatial engineering.

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• Electron-phonon coupling
• Phonons
• Graphene
• Tight-binding model