The Minimum Matching Energy of Bicyclic Graphs with given Girth
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چکیده
The matching energy of a graph was introduced by Gutman and Wagner in 2012 and defined as the sum of the absolute values of zeros of its matching polynomial. Let θ(r, s, t) be the graph obtained by fusing two triples of pendant vertices of three paths Pr+2, Ps+2 and Pt+2 to two vertices. The graph obtained by identifying the center of the star Sn−g with the degree 3 vertex u of θ(1, g−3, 1) is denoted by Sn−g(u)θ(1, g−3, 1). In this paper, we show that, Sn−g(u)θ(1, g − 3, 1) has minimum matching energy among all bicyclic graphs with order n and girth g.
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تاریخ انتشار 2016