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The extremal unicyclic graphs with given diameter and minimum edge revised Szeged index
AIMS Mathematics 2023, 8(11): 26301-26327
Published: 15 November 2023
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Let H be a connected graph. The edge revised Szeged index of H is defined as S z e ( H ) = e = u v E H ( m u ( e | H ) + m 0 ( e | H ) 2 ) ( m v ( e | H ) + m 0 ( e | H ) 2 ), where m u ( e | H ) (resp., m v ( e | H )) is the number of edges whose distance to vertex u (resp., v) is smaller than to vertex v (resp., u), and m 0 ( e | H ) is the number of edges equidistant from u and v. In this paper, the extremal unicyclic graphs with given diameter and minimum edge revised Szeged index are characterized.

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