Characterizing potentially ar+1- Mk2-graphic sequences

Abstract

If π = (d₁,d₂, ... ,d_n)ε GS _n has a realization G with the vertex set V(G) = {v ₁,v₂.... V_n } such that dG{v_t) = d, for 1 ≤ i < n and G[{v₁,V₂,....,v_r+1}] = K_r+1 - mK₂ such that dk_r+1-mk₂(v) = r for 1 ≤ i ≤ r+1-2m and dK_r+1-mK2(v_t) = r-1 for r+2-2m ≤i ≤ r + 1, then π is said to be potentially A_r+1- mK₂-graphic. n this paper, we characterize the potentially A _r+1-mK₂(1 ≤ m ≤ [r+1/2])graphic sequences.