scholarly journals Seidel Switching and Graph Energy

2012 ◽  
Author(s):  
Willem H. Haemers
Keyword(s):  
Graph Energy ◽  
Seidel Switching

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 .

scholarly journals Protein Sequence Comparison Based on Physicochemical Properties and the Position-Feature Energy Matrix

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Lulu Yu ◽  
Yusen Zhang ◽  
Ivan Gutman ◽  
Yongtang Shi ◽  
Matthias Dehmer
Keyword(s):  
Physicochemical Properties ◽  
Protein Sequence ◽  
Sequence Comparison ◽  
Protein Sequences ◽  
Local Dynamic ◽  
Order Information ◽  
Energy Matrix ◽  
Graph Energy ◽  
Feature Based ◽  
Protein Sequence Comparison

Abstract We develop a novel position-feature-based model for protein sequences by employing physicochemical properties of 20 amino acids and the measure of graph energy. The method puts the emphasis on sequence order information and describes local dynamic distributions of sequences, from which one can get a characteristic B-vector. Afterwards, we apply the relative entropy to the sequences representing B-vectors to measure their similarity/dissimilarity. The numerical results obtained in this study show that the proposed methods leads to meaningful results compared with competitors such as Clustal W.

Classification for Microarray Data Based on K-Means Clustering Combined with Modified Single-to-Noise-Ratio Based on Graph Energy

2017 ◽  
Vol 14 (1) ◽  
pp. 598-606 ◽  
Author(s):  
Lujing Yu ◽  
Yusen Zhang ◽  
Guiqian Jian ◽  
Ivan Gutman
Keyword(s):  
Microarray Data ◽  
Classification Performance ◽  
Small Subset ◽  
New Classification ◽  
Dna Microarray Data ◽  
Sample Classification ◽  
Graph Energy ◽  
Noise Ratio ◽  
Characteristic Features ◽  
Training Examples

This paper proposes a new classification for microarray data which utilizes K-means clustering combined with modified single-to-noise-ratio based on graph energy (SNRGE) method. This method is employed to select a small subset of characteristic features from DNA microarray data. Comparing with the single-to-noise-ratio (SNR) method proposed by Golub, it demonstrates that the SNRGES outperforms SNR method. SNRGE obtains significant improvement on the classification result via SNRGES in contrast with other SNR formulas, and the result shows that the use of SNRGE formula is critical in eliminating irrelevant features. As compared to other feature selection methods via five classifiers, the SNRGES yields better classification performance. On available training examples from four microarray databases, we indicate that SNRGES is capable of achieving better accuracies than previous studies, and is able to effectively remove redundant features and obtain efficient sets for sample classification purposes.

scholarly journals Estimating vertex-degree-based energies

2022 ◽  
Vol 70 (1) ◽  
pp. 13-23
Author(s):  
Ivan Gutman
Keyword(s):  
General Theory ◽  
Spectral Theory ◽  
Current Literature ◽  
Bipartite Graphs ◽  
Upper Bounds ◽  
Vertex Degree ◽  
Lower And Upper Bounds ◽  
Graph Invariants ◽  
General Properties ◽  
Graph Energy

Introduction/purpose: In the current literature, several dozens of vertex-degree-based (VDB) graph invariants are being studied. To each such invariant, a matrix can be associated. The VDB energy is the energy (= sum of the absolute values of the eigenvalues) of the respective VDB matrix. The paper examines some general properties of the VDB energy of bipartite graphs. Results: Estimates (lower and upper bounds) are established for the VDB energy of bipartite graphs in which there are no cycles of size divisible by 4, in terms of ordinary graph energy. Conclusion: The results of the paper contribute to the spectral theory of VDB matrices, especially to the general theory of VDB energy.

scholarly journals Dissecting molecular network structures using a network subgraph approach

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9556
Author(s):  
Chien-Hung Huang ◽  
Efendi Zaenudin ◽  
Jeffrey J.P. Tsai ◽  
Nilubon Kurubanjerdjit ◽  
Eskezeia Y. Dessie ◽  
...  
Keyword(s):  
Biological Networks ◽  
Spectral Graph Theory ◽  
Molecular Networks ◽  
Driver Genes ◽  
Complexity Measures ◽  
Cellular Processes ◽  
Graph Energy ◽  
Energy Cutoff ◽  
Cancer Networks ◽  
Irreducible Graphs

Biological processes are based on molecular networks, which exhibit biological functions through interactions of genetic elements or proteins. This study presents a graph-based method to characterize molecular networks by decomposing the networks into directed multigraphs: network subgraphs. Spectral graph theory, reciprocity and complexity measures were used to quantify the network subgraphs. Graph energy, reciprocity and cyclomatic complexity can optimally specify network subgraphs with some degree of degeneracy. Seventy-one molecular networks were analyzed from three network types: cancer networks, signal transduction networks, and cellular processes. Molecular networks are built from a finite number of subgraph patterns and subgraphs with large graph energies are not present, which implies a graph energy cutoff. In addition, certain subgraph patterns are absent from the three network types. Thus, the Shannon entropy of the subgraph frequency distribution is not maximal. Furthermore, frequently-observed subgraphs are irreducible graphs. These novel findings warrant further investigation and may lead to important applications. Finally, we observed that cancer-related cellular processes are enriched with subgraph-associated driver genes. Our study provides a systematic approach for dissecting biological networks and supports the conclusion that there are organizational principles underlying molecular networks.

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