Vertex PI indices of four sums of graphs

Suppose that ee is an edge of a graph GG. Denote by me(G)me(G) the number of vertices of GG that are not equidistant from both ends of ee. Then the vertex PI index of GG is defined as the summation of me(G)me(G) over all edges ee of GG. In this paper we give the explicit expressions for the vertex PI indices of four sums of two graphs in terms of other indices of two individual graphs, which correct the main results in a paper published in Ars Combin. 98 (2011).

► Suppose that e=uve=uv is an edge of a graph GG.
► Let me(G)me(G) be the number of vertices of GG that are not equidistant from uu and vv.
► Then the vertex PI index of GG is defined as ∑e∈E(G)me(G)∑e∈E(G)me(G).
► In this paper we give the formulae for the vertex PI indices of four sums of graphs.
► This corrects the main results in a paper published in Ars Combin. 98 (2011).