C4 Free Detour Distance

Abstract

For every connected graph G, the square free detour distance SFD  (u, v) is the length of a longest u- v square free path in G, where u, v are the vertices of G.  A u-v square free path of length SFD(u, v) is called the u-v square free detour. It is found that the square free detour distance differs from the  distance  , monophonic distance and  detour distance. The square free detour distance is found for some standard graphs. Their bounds are determined and their sharpness is checked. Certain general properties satisfied by them are studied.