On Omega Index and Average Degree of Graphs
Average degree of a graph is defined to be a graph invariant equal to the arithmetic mean of all vertex degrees and has many applications, especially in determining the irregularity degrees of networks and social sciences. In this study, some properties of average degree have been studied. Effect of...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5565146 |
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| _version_ | 1832559936287014912 |
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| author | Sadik Delen Musa Demirci Ahmet Sinan Cevik Ismail Naci Cangul |
| author_facet | Sadik Delen Musa Demirci Ahmet Sinan Cevik Ismail Naci Cangul |
| author_sort | Sadik Delen |
| collection | DOAJ |
| description | Average degree of a graph is defined to be a graph invariant equal to the arithmetic mean of all vertex degrees and has many applications, especially in determining the irregularity degrees of networks and social sciences. In this study, some properties of average degree have been studied. Effect of vertex deletion on this degree has been determined and a new proof of the handshaking lemma has been given. Using a recently defined graph index called omega index, average degree of trees, unicyclic, bicyclic, and tricyclic graphs have been given, and these have been generalized to k-cyclic graphs. Also, the effect of edge deletion has been calculated. The average degree of some derived graphs and some graph operations have been determined. |
| format | Article |
| id | doaj-art-e0eff990b4c94dee9cc55d6d187875f6 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e0eff990b4c94dee9cc55d6d187875f62025-02-03T01:28:55ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/5565146On Omega Index and Average Degree of GraphsSadik Delen0Musa Demirci1Ahmet Sinan Cevik2Ismail Naci Cangul3Faculty of Arts and ScienceFaculty of Arts and ScienceFaculty of ScienceFaculty of Arts and ScienceAverage degree of a graph is defined to be a graph invariant equal to the arithmetic mean of all vertex degrees and has many applications, especially in determining the irregularity degrees of networks and social sciences. In this study, some properties of average degree have been studied. Effect of vertex deletion on this degree has been determined and a new proof of the handshaking lemma has been given. Using a recently defined graph index called omega index, average degree of trees, unicyclic, bicyclic, and tricyclic graphs have been given, and these have been generalized to k-cyclic graphs. Also, the effect of edge deletion has been calculated. The average degree of some derived graphs and some graph operations have been determined.http://dx.doi.org/10.1155/2021/5565146 |
| spellingShingle | Sadik Delen Musa Demirci Ahmet Sinan Cevik Ismail Naci Cangul On Omega Index and Average Degree of Graphs Journal of Mathematics |
| title | On Omega Index and Average Degree of Graphs |
| title_full | On Omega Index and Average Degree of Graphs |
| title_fullStr | On Omega Index and Average Degree of Graphs |
| title_full_unstemmed | On Omega Index and Average Degree of Graphs |
| title_short | On Omega Index and Average Degree of Graphs |
| title_sort | on omega index and average degree of graphs |
| url | http://dx.doi.org/10.1155/2021/5565146 |
| work_keys_str_mv | AT sadikdelen onomegaindexandaveragedegreeofgraphs AT musademirci onomegaindexandaveragedegreeofgraphs AT ahmetsinancevik onomegaindexandaveragedegreeofgraphs AT ismailnacicangul onomegaindexandaveragedegreeofgraphs |