Minimality considerations for graph energy over a class of graphs
Dongdong Wang,Hongbo Hua +1 more
TLDR
The graphs in U"n^1 with minimal and second-minimal energies are uniquely determined, respectively.Abstract:
Let G be a graph on n vertices, and let CHP(G;@l) be the characteristic polynomial of its adjacency matrix A(G). All n roots of CHP(G;@l), denoted by @l"i(i=1,2,...n), are called to be its eigenvalues. The energy E(G) of a graph G, is the sum of absolute values of all eigenvalues, namely, E(G)=@?"i"="1^n|@l"i|. Let U"n be the set of n-vertex unicyclic graphs, the graphs with n vertices and n edges. A fully loaded unicyclic graph is a unicyclic graph taken from U"n with the property that there exists no vertex with degree less than 3 in its unique cycle. Let U"n^1 be the set of fully loaded unicyclic graphs. In this article, the graphs in U"n^1 with minimal and second-minimal energies are uniquely determined, respectively.read more
Citations
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Book ChapterDOI
The energy of random graphs
Wenxue Du,Xueliang Li,Yiyang Li +2 more
TL;DR: In this paper, an exact estimate of the energy of random bipartite graphs G n (p) was established, by using the Wigner semicircle law for any probability p. But only a few graphs attain the equalities in these bounds.
Book ChapterDOI
Bounds for the Energy of Graphs
TL;DR: In this paper, the graph eigenvalues are labeled in a nonincreasing manner, i.e., λ1≥λ2≥⋯≥ λ n.
Journal ArticleDOI
On maximal energy and hosoya index of trees without perfect matching
TL;DR: In this paper, a counterexample to Ou's results was provided, where the maximal element with respect to E(G) and Hosoya index was shown to be maximal among the nonconjugated n-vertex trees in the case of even n.
Book ChapterDOI
Hyperenergetic and Equienergetic Graphs
TL;DR: In this article, it was shown that for almost all graphs, the energy of the n-vertex complete graph K n is equal to 2(n − 1), where n is the number of vertices in the graph.
Book ChapterDOI
The Chemical Connection
TL;DR: A method for finding approximate solutions of the Schrodinger equation of a class of organic molecules, the so-called conjugated hydrocarbons, was proposed by the German scholar Erich Huckel as discussed by the authors.
References
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Book
Mathematical concepts in organic chemistry
Ivan Gutman,Oskar E. Polansky +1 more
TL;DR: In this paper, the authors define the topology of a graph as follows: 1.1 Topology in Chemistry, 2.2 Geometry, Symmetry, Topology, Graph Automorphisms, and Graph Topology.
Book ChapterDOI
The Energy of a Graph: Old and New Results
TL;DR: In this article, the energy of a graph G is defined as the sum of the absolute values of the eigenvalues of G. The connection between E and the total electron energy of organic molecules is briefly outlined.
Journal ArticleDOI
Acyclic systems with extremal Hückel π-electron energy
TL;DR: Among acyclic polyenes CnHn+2, the linear isomer H2C=(CH)n−2=CH2 has maximal HMO π-electron energy as mentioned in this paper.
Journal ArticleDOI
Topology and stability of conjugated hydrocarbons: The dependence of total π-electron energy on molecular topology
TL;DR: In spite of the fact that research on the mathematical properties of the total π-electron energy (as computed by means of the Huckel molecular orbital approximation) started already in the 1940s, many results in this area have been obtained also in the newest times.
Journal ArticleDOI
Unicyclic Graphs with Minimal Energy
TL;DR: In this article, it was shown that S.............. n====== n====== �� 3 is the unique minimal energy graph among all unicyclic graphs with n vertices (n≥6).