TO FIND ALL THE 1-FACTORS AND 1-FACTORIAL CONNECTIONS OF A FLOW GRAPH

This note gives a method to find all the 1-factors and 1-factorial connections of a flow graph. Let (D) be the set of all subgraphs of a given diagraph G(V, E) and (H) be the set of all subsets of (D). For h1, h2 (H), a multiplication operation being called star is denoted by the symbol * and is defined in the following: h1,*h2 ={xy/xh1, yh2, and deg+xy(i)2, deg-xy(i)2}. Theorem Let G(V, E) be a diagraph with vertex set V={1, 2,,}, and let Sk={(k, t)/(k, t) E, t V}. Then all the 1-factors of G(V,E) can be determined by the product of Sk as follows:C=S1*S2**S Obviously, if G(V,E) is replaced by G(V, E) is replaced by G(V, E)U(j, i), (j, i) E, then the product gives all the 1-factorial connections from em to j of the diagraph G(V, E).