Helly Number, Radon Number and Rank in $\mathrm{\Delta }$-Convexity on Graphs

This article discusses $\mathrm{\Delta }$-convexity on simple connected graphs. We establish general bounds for the Helly number, Radon number, and rank with respect to $\mathrm{\Delta }$-convexity on graphs. Additionally, we give the exact values for the Helly number and Radon number for chordal graphs, as well as the rank for block graphs.