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In recent years, much attention has been paid to γ-graphynes due to their high potential in practical applications. The unique combination of sp2–sp carbon atoms, an extended π-conjugated structure and evenly distributed dehydrobenzo[n]annulene pores provide excellent performance of γ-graphynes in gas separation, water purification, sensors, and catalysis. In this work, we report the ground and excited state properties of γ-graphyne, γ-graphdiyne, and γ-graphtriyne and their non-covalent complexes with fullerenes. Our results demonstrate that the non-covalent complexes are stable and exhibit low mobility of C 60 across the graphtriyne sheet. The electron-withdrawing ability of these materials is enhanced by passing from γ-graphyne to γ-graphtriyne, which assists in photoinduced electron transfer from endohedral fullerenes to graphyne. The process is found to occur on a sub-nanosecond time scale in the complexes of γ-graphdiyne and γ-graphtriyne with Sc 3 N@C 80. These theoretical results provide useful insights for the development of carbon materials for photovoltaic applications. [Display omitted] • Electron-withdrawing character of γ-graphyne materials is enhanced when moving from γ-graphyne to γ-graphtriyne. • Extended acetylene linkages between phenyl rings reduce the movement of fullerene over γ-graphyne surface. • Photoinduced electron transfer in the complexes of γ−graphyne with fullerene is facilitated by replacing C 60 with Sc 3 N@C 80. • Lowest charge transfer states correspond to the electron transfer from endohedral fullerene to γ-graphyne. [ABSTRACT FROM AUTHOR]