Extremum Modified First Zagreb Connection Index of n-Vertex Trees with Fixed Number of Pendent Vertices
The modified first Zagreb connection index ZC1∗ is a graph invariant that appeared about fifty years ago within a study of molecular modeling, and after a long time, it has been revisited in two papers ((Ali and Trinajstić, 2018) and (Naji et al., 2017)) independently. For a graph G, this graph inva...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/3295342 |
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| author | Sadia Noureen Akhlaq Ahmad Bhatti Akbar Ali |
| author_facet | Sadia Noureen Akhlaq Ahmad Bhatti Akbar Ali |
| author_sort | Sadia Noureen |
| collection | DOAJ |
| description | The modified first Zagreb connection index ZC1∗ is a graph invariant that appeared about fifty years ago within a study of molecular modeling, and after a long time, it has been revisited in two papers ((Ali and Trinajstić, 2018) and (Naji et al., 2017)) independently. For a graph G, this graph invariant is defined as ZC1∗G=∑v∈VGdvτv, where dv is the degree of the vertex v and τv is the connection number of v (that is, the number of vertices having distance 2 from v). In this paper, the graphs with maximum/minimum ZC1∗ value are characterized from the class of all n-vertex trees with fixed number of pendent vertices (that are the vertices of degree 1). |
| format | Article |
| id | doaj-art-31829795b064432c8e254e906b59d4c1 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-31829795b064432c8e254e906b59d4c12025-02-03T06:43:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/32953423295342Extremum Modified First Zagreb Connection Index of n-Vertex Trees with Fixed Number of Pendent VerticesSadia Noureen0Akhlaq Ahmad Bhatti1Akbar Ali2Department of Mathematics, National University of Computer and Emerging Sciences, Lahore, PakistanDepartment of Mathematics, National University of Computer and Emerging Sciences, Lahore, PakistanDepartment of Mathematics, Faculty of Science, University of Ha’il, Ha’il, Saudi ArabiaThe modified first Zagreb connection index ZC1∗ is a graph invariant that appeared about fifty years ago within a study of molecular modeling, and after a long time, it has been revisited in two papers ((Ali and Trinajstić, 2018) and (Naji et al., 2017)) independently. For a graph G, this graph invariant is defined as ZC1∗G=∑v∈VGdvτv, where dv is the degree of the vertex v and τv is the connection number of v (that is, the number of vertices having distance 2 from v). In this paper, the graphs with maximum/minimum ZC1∗ value are characterized from the class of all n-vertex trees with fixed number of pendent vertices (that are the vertices of degree 1).http://dx.doi.org/10.1155/2020/3295342 |
| spellingShingle | Sadia Noureen Akhlaq Ahmad Bhatti Akbar Ali Extremum Modified First Zagreb Connection Index of n-Vertex Trees with Fixed Number of Pendent Vertices Discrete Dynamics in Nature and Society |
| title | Extremum Modified First Zagreb Connection Index of n-Vertex Trees with Fixed Number of Pendent Vertices |
| title_full | Extremum Modified First Zagreb Connection Index of n-Vertex Trees with Fixed Number of Pendent Vertices |
| title_fullStr | Extremum Modified First Zagreb Connection Index of n-Vertex Trees with Fixed Number of Pendent Vertices |
| title_full_unstemmed | Extremum Modified First Zagreb Connection Index of n-Vertex Trees with Fixed Number of Pendent Vertices |
| title_short | Extremum Modified First Zagreb Connection Index of n-Vertex Trees with Fixed Number of Pendent Vertices |
| title_sort | extremum modified first zagreb connection index of n vertex trees with fixed number of pendent vertices |
| url | http://dx.doi.org/10.1155/2020/3295342 |
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