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adj忧郁的

https://doi.org/10.1007/978-3-319-72781-3In this chapter we have collected results on graph energy that could not be outlined elsewhere.

ATP861

The Coulson Integral Formula,In the theory of graph energy, the so-called . (3.1) plays an outstanding role. This formula was obtained by Charles Coulson as early as 1940 [73] and reads: . where . is a graph, ϕ(.,.) is the characteristic polynomial of ., ϕ.(.,.)=(d∕d.)ϕ(.,.) its first derivative, and ..

一大群

异端

Miscellaneous,In this chapter we have collected results on graph energy that could not be outlined elsewhere.

变量

Introduction, by ..,..,.,... The adjacency matrix .(.) of the graph . is a square matrix of order ., whose (.,.)-entry is equal to 1 if the vertices .. and .. are adjacent and is equal to zero otherwise. The characteristic polynomial of the adjacency matrix, i.e., det(...−.(.)), where .. is the unit matrix of or

uncertain

不遵守

Common Proof Methods,est bounds for the energy within some special classes of graphs and graphs from these classes with extremal values of energy. Finding answers to such questions is often far from elementary. In this chapter we outline some fundamental methods that are frequently used for solving problems of this kind

抵押贷款

Bounds for the Energy of Graphs, i.e., λ.≥λ.≥⋯≥λ.. If . is connected, then λ.>λ. [81]. Because λ.≥|λ.|,.=2,.,., the eigenvalue λ. is referred to as the . of .. Three well-known relations for the eigenvalues are . The following lemma [81] will be frequently used in the proofs:

sed-rate

The Energy of Random Graphs,cular interest. But only a few graphs attain the equalities in these bounds. In [105], an exact estimate of the energy of random graphs ..(.) was established, by using the Wigner semicircle law for any probability .. Furthermore, in [105], the energy of random multipartite graphs was investigated, b

syncope

Graphs Extremal with Regard to Energy,lues. The first such result was obtained for trees in[145], where it was demonstrated that the star has minimal and the path maximal energy. In the meantime, a remarkably large number of papers was published on such extremal problems: for general graphs [82, 242, 252, 253, 305, 306, 341, 416, 482],