Hyperenergetic and Equienergetic Graphs

Xueliang Li, Yongtang Shi and Ivan Gutman
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Xueliang Li: Nankai University, Center for Combinatorics
Yongtang Shi: Nankai University, Center for Combinatorics
Ivan Gutman: University of Kragujevac, Faculty of Science

Chapter Chapter 8 in Graph Energy, 2012, pp 193-201 from Springer

Abstract: Abstract The energy of the n-vertex complete graph K n is equal to 2(n − 1). We call an n-vertex graph Ghyperenergetic if ℰ(G) > 2(n − 1). From Theorem 5.24, we know that for almost all graphs, $$\mathcal{E}(G) > \left (\frac{1} {4} + o(1)\right ){n}^{3/2}$$ , which means that almost all graphs are hyperenergetic. Therefore, any search for hyperenergetic graphs nowadays is a futile task. Yet, before Theorem 5.24 was discovered, a number of such results were obtained. We outline here some of them; for surveys, see [41, 178].

Keywords: Circle Graphs; Kneser Graph; Middle Vertex; Small Triplet; Iterated Line Graphs (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-4220-2_8

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