Proximity and remoteness in triangle-free and C4-free graphs in terms of order and minimum degree

Let G be a finite, connected graph. The average distance of vertex v is the arithmetic mean distances from to all other vertices . remoteness ? ( ) and proximity ? are maximum minimum In this paper, we present sharp upper bound on triangle-free graph given order degree, corresponding proximity, which apart an additive constant. We also bounds C 4 -free graphs demonstrate that these close being best possible.