The maximum matching energy of bicyclic graphs with even girth
نویسندگان
چکیده
منابع مشابه
The Minimum Matching Energy of Bicyclic Graphs with given Girth
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 ...
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Let G be a simple graph of order n, let λ1(G), λ2(G), . . . , λn(G) be the eigenvalues of the adjacency matrix of G. The Esrada index of G is defined as EE(G) = ∑n i=1 e i. In this paper we determine the unique graph with maximum Estrada index among bicyclic graphs with fixed order.
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The harmonic index of a graph $G$, denoted by $H(G)$, is defined asthe sum of weights $2/[d(u)+d(v)]$ over all edges $uv$ of $G$, where$d(u)$ denotes the degree of a vertex $u$. Hu and Zhou [Y. Hu and X. Zhou, WSEAS Trans. Math. {bf 12} (2013) 716--726] proved that for any bicyclic graph $G$ of order $ngeq 4$, $H(G)le frac{n}{2}-frac{1}{15}$ and characterize all extremal bicyclic graphs.In this...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2016.01.020