Quality Index of Balanced Digraphs
نویسنده
چکیده
Let G be a multidigraph with vertices V (G) and arcs A(G). G is balanced if d+G(v) = d − G(v) for every v ∈ V (G). Let ri, rj be the number of cycles in G that include ai, aj ∈ A(G) respectively, and ri ≥ rj. Local quality index of G is defined as the largest ratio ri rj for opposite arcs ai, aj . Global quality index of G is defined as the largest ratio ri rj for distinct arcs ai, aj . In this work we prove that for balanced multidigraphs only a local quality index can have a finite upper bound, and it exists when we are not limited to considering only simple cycles. In addition, we prove that 32 is the best upper bound in such case and it is not attainable by a finite balanced multidigraph. Mathematics Subject Classification: 05C85
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