scholarly journals Graph energy and nullity

2021 ◽  
Vol 4 (1) ◽  
pp. 25-28
Author(s):  
Ivan Gutman ◽  
Keyword(s):  
Algebraic Multiplicity ◽  
Graph Energy

The energy of a graph is the sum of absolute values of its eigenvalues. The nullity of a graph is the algebraic multiplicity of number zero in its spectrum. Empirical facts indicate that graph energy decreases with increasing nullity, but proving this property is difficult. In this paper, a method is elaborated by means of which the effect of nullity on graph energy can be quantitatively estimated.

The deformation multiplicity of a map germ with respect to a Boardman symbol

2001 ◽  
Vol 131 (5) ◽  
pp. 1003-1022 ◽  
Author(s):  
C. Bivià-Ausina ◽  
J. J. Nuño-Ballesteros
Keyword(s):  
Geometrical Interpretation ◽  
Algebraic Multiplicity ◽  
Homogeneous Map

We define the deformation multiplicity of a map germ f: (Cn, 0) → (Cp, 0) with respect to a Boardman symbol i of codimension less than or equal to n and establish a geometrical interpretation of this number in terms of the set of Σi points that appear in a generic deformation of f. Moreover, this number is equal to the algebraic multiplicity of f with respect to i when the corresponding associated ring is Cohen-Macaulay. Finally, we study how algebraic multiplicity behaves with weighted homogeneous map germs.

A lower bound for graph energy

2018 ◽  
Vol 68 (8) ◽  
pp. 1624-1632
Author(s):  
Qi Zhou ◽  
Dein Wong ◽  
Dongqin Sun
Keyword(s):  
Lower Bound ◽  
Graph Energy

scholarly journals Graph energy change due to any single edge deletion

2015 ◽  
Vol 29 ◽  
pp. 59-73
Author(s):  
Wen-Huan Wang ◽  
Wasin So
Keyword(s):  
Partial Solution ◽  
Energy Change ◽  
Single Edge ◽  
Edge Deletion ◽  
Numerical Evidence ◽  
Graph Energy ◽  
The Absolute ◽  
Cycle Graph

The energy of a graph is the sum of the absolute values of its eigenvalues. We propose a new problem on graph energy change due to any single edge deletion. Then we survey the literature for existing partial solution of the problem, and mention a conjecture based on numerical evidence. Moreover, we prove in three different ways that the energy of a cycle graph decreases when an arbitrary edge is deleted except for the order of 4.

scholarly journals The asymptotic value of graph energy for random graphs with degree-based weights

2020 ◽  
Vol 284 ◽  
pp. 481-488 ◽  
Author(s):  
Xueliang Li ◽  
Yiyang Li ◽  
Jiarong Song
Keyword(s):  
Random Graphs ◽  
Asymptotic Value ◽  
Graph Energy

scholarly journals Extremal Chemical Trees

2002 ◽  
Vol 57 (1-2) ◽  
pp. 49-51
Author(s):  
Miranca Fischermann ◽  
Ivan Gutman ◽  
Arne Hoffmann ◽  
Dieter Rautenbach ◽  
Dušica Vidovića ◽  
...  
Keyword(s):  
Carbon Atom ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Wiener Index ◽  
Graph Representation ◽  
Hosoya Index ◽  
Saturated Hydrocarbons ◽  
Physico Chemical ◽  
Graph Energy ◽  
Chemical Trees

A variety of molecular-graph-based structure-descriptors were proposed, in particular the Wiener index W. the largest graph eigenvalue λ1, the connectivity index X, the graph energy E and the Hosoya index Z, capable of measuring the branching of the carbon-atom skeleton of organic compounds, and therefore suitable for describing several of their physico-chemical properties. We now determine the structure of the chemical trees (= the graph representation of acyclic saturated hydrocarbons) that are extremal with respect to W , λ1, E, and Z. whereas the analogous problem for X was solved earlier. Among chemical trees with 5. 6, 7, and 3k + 2 vertices, k = 2,3,..., one and the same tree has maximum λ1 and minimum W, E, Z. Among chemical trees with 3k and 3k +1 vertices, k = 3,4...., one tree has minimum 11 and maximum λ1 and another minimum E and Z .

The algebraic multiplicity of the complex eigenvalues of population operator and its application

2001 ◽  
Vol 80 (3-4) ◽  
pp. 257-268
Author(s):  
Xue-Zhi Li ◽  
Geni Gupur ◽  
Chun-Lei Tang ◽  
Guang-Tian Zhu
Keyword(s):  
Algebraic Multiplicity ◽  
Complex Eigenvalues
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