This paper solves the computing problems of Balaban index for 3-regular graph Ln.By using the method of classification discussion,a formula for the Balaban index of Ln is given and the upper and lower bounds that are easy to compute is acquired from this formula.The results show that the upper bound obtained in this paper is superior to the existing one,and if the order is greater than or equal to 42,the difference between the upper bound and the exact value is less than 0.1.
Balaban index3-regular graphdistanceupper and lower bound
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