Upper bounds for the extended energy of graphs and some extended equienergetic graphs
نویسندگان
چکیده
منابع مشابه
Some upper bounds for the energy of graphs
LetG = (V, E)be a graphwith n vertices and e edges.Denote V (G) = {v1, v2, . . . , vn}. The 2-degree of vi , denoted by ti , is the sum of degrees of the vertices adjacent to vi , 1 i n. Let σi be the sum of the 2-degree of vertices adjacent to vi . In this paper, we present two sharp upper bounds for the energy of G in terms of n, e, ti , and σi , from which we can get some known results. Also...
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In this paper, we obtain some upper and lower bounds for the general extended energy of a graph. As an application, we obtain few bounds for the (edge) Zagreb energy of a graph. Also, we deduce a relation between Zagreb energy and edge-Zagreb energy of a graph $G$ with minimum degree $delta ge2$. A lower and upper bound for the spectral radius of the edge-Zagreb matrix is obtained. Finally, we ...
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LetG be a finite, simple, and undirected graphwith n vertices. Thematrix L(G) = D(G)−A(G) (resp., L+(G) = D(G)+A(G)) is called the Laplacianmatrix (resp., signless Laplacianmatrix [1–4]) of G, where A(G) is the adjacency matrix and D(G) is the diagonal matrix of the vertex degrees. (For details on Laplacian matrix, see [5, 6].) Since A(G), L(G) and L+(G) are all real symmetric matrices, their e...
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ژورنال
عنوان ژورنال: Opuscula Mathematica
سال: 2018
ISSN: 1232-9274
DOI: 10.7494/opmath.2018.38.1.5