Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs. (16th April 2019) - Chen, Xiaolin; Lian, Huishu
Abstract : The matching energyM E ( G ) of a graphG was introduced by Gutman and Wagner, which is defined as the sum of the absolute values of the roots of the matching polynomialm ( G, x ) . The largest matching rootλ 1 ( G ) is the largest root of the matching polynomialm ( G, x ) . LetK n 1, n 2, …, n r denote the completer -partite graph with ordern = n 1 + n 2 + … + n r, wherer > 1 . In this paper, we prove that, for the given valuesn andr, both the matching energyM E ( G ) and the largest matching rootλ 1 ( G ) of completer -partite graphs are minimal for complete split graphC S ( n, r - 1 ) and are maximal for Turán graphT ( n, r ) .