For an integer s ≤ 1, an s-arc in a graph G is a sequence of (s + 1) vertices (v 1 , v 2 , ..., v s , v s +1) of G such that for all 1 ≤ i ≤ s, v i ~ v i+1 , and for all 1 ≤ i ≤ s – 1, v i ≠ v i+2 . A non-intersection graph of the set of all s-arcs on distinct vertices of G, that can be shunted onto some other s-arc on distinct vertices of G, has been introduced. Basic properties based on the order, size and the degree of the graph defined is obtained. Additionally, certain properties pertaining to the connectedness of the same is discussed.
Prebhath et al. (Fri,) studied this question.