Graph Entropy Based on Strong Coloring of Uniform Hypergraphs
The classical graph entropy based on the vertex coloring proposed by <i>Mowshowitz</i> depends on a graph. In fact, a hypergraph, as a generalization of a graph, can express complex and high-order relations such that it is often used to model complex systems. Being different from the cla...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-12-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/11/1/3 |
| _version_ | 1827666687536660480 |
|---|---|
| author | Lusheng Fang Bo Deng Haixing Zhao Xiaoyun Lv |
| author_facet | Lusheng Fang Bo Deng Haixing Zhao Xiaoyun Lv |
| author_sort | Lusheng Fang |
| collection | DOAJ |
| description | The classical graph entropy based on the vertex coloring proposed by <i>Mowshowitz</i> depends on a graph. In fact, a hypergraph, as a generalization of a graph, can express complex and high-order relations such that it is often used to model complex systems. Being different from the classical graph entropy, we extend this concept to a hypergraph. Then, we define the graph entropy based on the vertex strong coloring of a hypergraph. Moreover, some tightly upper and lower bounds of such graph entropies as well as the corresponding extremal hypergraphs are obtained. |
| first_indexed | 2024-03-10T01:55:13Z |
| format | Article |
| id | doaj.art-a7594fbe43514a8e95c26a5ee8fe5728 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T01:55:13Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-a7594fbe43514a8e95c26a5ee8fe57282023-11-23T12:58:01ZengMDPI AGAxioms2075-16802021-12-01111310.3390/axioms11010003Graph Entropy Based on Strong Coloring of Uniform HypergraphsLusheng Fang0Bo Deng1Haixing Zhao2Xiaoyun Lv3School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, ChinaSchool of Mathematics and Statistics, Qinghai Normal University, Xining 810001, ChinaThe State Key Laboratory of Tibetan Information Processing and Application, Xining 810008, ChinaSchool of Mathematics and Statistics, Qinghai Normal University, Xining 810001, ChinaThe classical graph entropy based on the vertex coloring proposed by <i>Mowshowitz</i> depends on a graph. In fact, a hypergraph, as a generalization of a graph, can express complex and high-order relations such that it is often used to model complex systems. Being different from the classical graph entropy, we extend this concept to a hypergraph. Then, we define the graph entropy based on the vertex strong coloring of a hypergraph. Moreover, some tightly upper and lower bounds of such graph entropies as well as the corresponding extremal hypergraphs are obtained.https://www.mdpi.com/2075-1680/11/1/3hypergraphgraph entropystrong coloring |
| spellingShingle | Lusheng Fang Bo Deng Haixing Zhao Xiaoyun Lv Graph Entropy Based on Strong Coloring of Uniform Hypergraphs Axioms hypergraph graph entropy strong coloring |
| title | Graph Entropy Based on Strong Coloring of Uniform Hypergraphs |
| title_full | Graph Entropy Based on Strong Coloring of Uniform Hypergraphs |
| title_fullStr | Graph Entropy Based on Strong Coloring of Uniform Hypergraphs |
| title_full_unstemmed | Graph Entropy Based on Strong Coloring of Uniform Hypergraphs |
| title_short | Graph Entropy Based on Strong Coloring of Uniform Hypergraphs |
| title_sort | graph entropy based on strong coloring of uniform hypergraphs |
| topic | hypergraph graph entropy strong coloring |
| url | https://www.mdpi.com/2075-1680/11/1/3 |
| work_keys_str_mv | AT lushengfang graphentropybasedonstrongcoloringofuniformhypergraphs AT bodeng graphentropybasedonstrongcoloringofuniformhypergraphs AT haixingzhao graphentropybasedonstrongcoloringofuniformhypergraphs AT xiaoyunlv graphentropybasedonstrongcoloringofuniformhypergraphs |