Matching in Toeplitz graphs

For a sequence of positive integers n, t(1), t(2), . . . , t(k), with t(1), t(2), . . . , t(k) <= n - 1, the Toeplitz graph T-n < t(1), t(2), . . . , t(k)> is a graph on the vertex set {v(1), v(2), . . . , v(n)}, where the vertices v(i), v(j) are adjacent if and only if vertical bar i - j vertical bar is an element of {t(1), t(2), . . . , t(k)}. The matching number of a graph G, denoted by mu(G) is the size of a maximum matching in G. In this paper we introduce an algorithm to find a maximum matching in the graph T-n < s,t > for co-prime integers s, t, and discuss on the matching number of some families of Toeplitz graphs.