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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Autores principales:	Sadik Delen, Musa Demirci, Ahmet Sinan Cevik, Ismail Naci Cangul
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e0eff990b4c94dee9cc55d6d187875f6
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id	oai:doaj.org-article:e0eff990b4c94dee9cc55d6d187875f6
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spelling	oai:doaj.org-article:e0eff990b4c94dee9cc55d6d187875f62021-11-22T01:11:22ZOn Omega Index and Average Degree of Graphs2314-478510.1155/2021/5565146https://doaj.org/article/e0eff990b4c94dee9cc55d6d187875f62021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/5565146https://doaj.org/toc/2314-4785Average 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.Sadik DelenMusa DemirciAhmet Sinan CevikIsmail Naci CangulHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Sadik Delen Musa Demirci Ahmet Sinan Cevik Ismail Naci Cangul On Omega Index and Average Degree of Graphs
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
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
title	On Omega Index and Average Degree of Graphs
title_short	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_sort	on omega index and average degree of graphs
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/e0eff990b4c94dee9cc55d6d187875f6
work_keys_str_mv	AT sadikdelen onomegaindexandaveragedegreeofgraphs AT musademirci onomegaindexandaveragedegreeofgraphs AT ahmetsinancevik onomegaindexandaveragedegreeofgraphs AT ismailnacicangul onomegaindexandaveragedegreeofgraphs
_version_	1718418312627486720

On Omega Index and Average Degree of Graphs

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