The Average Eccentricity of Block Graphs: A Block Order Sequence Perspective
A graph is a <i>block graph</i> if its blocks are all cliques. In this paper, we study the average eccentricity of block graphs from the perspective of <i>block order sequences</i>. An equivalence relation is established under the block order sequence and used to prove the lo...
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MDPI AG
2022-03-01
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| Online Access: | https://www.mdpi.com/2075-1680/11/3/114 |
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| author | Xingfu Li Guihai Yu Kinkar Chandra Das |
| author_facet | Xingfu Li Guihai Yu Kinkar Chandra Das |
| author_sort | Xingfu Li |
| collection | DOAJ |
| description | A graph is a <i>block graph</i> if its blocks are all cliques. In this paper, we study the average eccentricity of block graphs from the perspective of <i>block order sequences</i>. An equivalence relation is established under the block order sequence and used to prove the lower and upper bounds of the eccentricity on block graphs. The result is that the lower and upper bounds of the average eccentricity on block graphs are 1 and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mn>1</mn><mi>n</mi></mfrac><mrow><mo>⌊</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><msup><mi>n</mi><mn>2</mn></msup><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>n</mi><mo>⌋</mo></mrow></mrow></semantics></math></inline-formula>, respectively, where <i>n</i> is the order of the block graph. Finally, we devise a linear time algorithm to calculate the block order sequence. |
| first_indexed | 2024-03-09T13:51:39Z |
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| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:51:39Z |
| publishDate | 2022-03-01 |
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| spelling | doaj.art-f6fd56e00ab1497c92f49eda9b9d2f9c2023-11-30T20:50:05ZengMDPI AGAxioms2075-16802022-03-0111311410.3390/axioms11030114The Average Eccentricity of Block Graphs: A Block Order Sequence PerspectiveXingfu Li0Guihai Yu1Kinkar Chandra Das2College of Big Data Statistics, Guizhou University of Finance and Economics, Guiyang 550025, ChinaCollege of Big Data Statistics, Guizhou University of Finance and Economics, Guiyang 550025, ChinaDepartment of Mathematics, Sungkyunkwan University, Suwon 16419, KoreaA graph is a <i>block graph</i> if its blocks are all cliques. In this paper, we study the average eccentricity of block graphs from the perspective of <i>block order sequences</i>. An equivalence relation is established under the block order sequence and used to prove the lower and upper bounds of the eccentricity on block graphs. The result is that the lower and upper bounds of the average eccentricity on block graphs are 1 and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mn>1</mn><mi>n</mi></mfrac><mrow><mo>⌊</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><msup><mi>n</mi><mn>2</mn></msup><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>n</mi><mo>⌋</mo></mrow></mrow></semantics></math></inline-formula>, respectively, where <i>n</i> is the order of the block graph. Finally, we devise a linear time algorithm to calculate the block order sequence.https://www.mdpi.com/2075-1680/11/3/114block order sequenceblock graphsaverage eccentricity |
| spellingShingle | Xingfu Li Guihai Yu Kinkar Chandra Das The Average Eccentricity of Block Graphs: A Block Order Sequence Perspective Axioms block order sequence block graphs average eccentricity |
| title | The Average Eccentricity of Block Graphs: A Block Order Sequence Perspective |
| title_full | The Average Eccentricity of Block Graphs: A Block Order Sequence Perspective |
| title_fullStr | The Average Eccentricity of Block Graphs: A Block Order Sequence Perspective |
| title_full_unstemmed | The Average Eccentricity of Block Graphs: A Block Order Sequence Perspective |
| title_short | The Average Eccentricity of Block Graphs: A Block Order Sequence Perspective |
| title_sort | average eccentricity of block graphs a block order sequence perspective |
| topic | block order sequence block graphs average eccentricity |
| url | https://www.mdpi.com/2075-1680/11/3/114 |
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