Graphs Extremal with Regard to Energy

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 7 in Graph Energy, 2012, pp 99-192 from Springer

Abstract: Abstract One of the fundamental questions that is encountered in the study of graph energy is which graphs (from a given class) have greatest and smallest $$\mathcal{E}$$ -values. 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], trees and chemical trees[141, 219, 268, 314, 316, 319, 324, 327, 339, 343, 344, 389, 390, 434, 435, 483, 487, 497, 498, 505, 506, 511, 517, 518, 543, 547], unicyclic[51, 58, 185, 191, 266, 270, 273–275, 277, 283, 312, 313, 330, 342, 480, 484–486, 488–490, 514], bicyclic[121, 267, 280, 340, 358, 500, 501, 522, 523], tricyclic [326, 329, 521], and tetracyclic graphs [325], as well as for benzenoid and related polycyclic systems [158, 243, 395, 399, 413–415, 519, 520, 526]. In this chapter we state a few of these results, selecting those that can be formulated in a simple manner or that otherwise deserve to be mentioned. We start with a few elementary results.

Keywords: Bicyclic Graphs; Coulson Integral Formula; Pendant Edge; Pendant Vertex; Pendent Paths (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-4220-2_7

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