Visibilities and sets of shortest paths in a connected graph
Ladislav Nebeský · Czechoslovak Mathematical Journal · 1995
By a graph we mean here an undirected (not necessarily finite) graph without loops and multiple edges.Thus if G is a graph with a vertex set V(G) and an edge setThe letters h, i, j, k, m and n will be reserved for denoting integers.Consider a graph G.We denote by W(G) the set of all finite sequences of vertices in G, including the empty sequence, which will be denoted by *.Thus W(G) -{*} is the set of all sequences (0) VQ, ..., Vj,where j ^ 0 and v 0 ,...,Vj G V(G). Similarly to [2], instead of (0) we will write VQ .. .Vj.Let UQ, ... ,U{,WQ, ... ,Wk G V(G), where i,k ^ 0, and let a =