Some Bond Incident Degree Indices of (Molecular) Graphs with Fixed Order and Number of Cut Vertices
A bond incident degree (BID) index of a graph G is defined as ∑uv∈EGfdGu,dGv, where dGw denotes the degree of a vertex w of G, EG is the edge set of G, and f is a real-valued symmetric function. The choice fdGu,dGv=adGu+adGv in the aforementioned formula gives the variable sum exdeg index SEIa, wher...
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/9970254 |
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| author | Abeer M. Albalahi Akbar Ali Tayyba Zafar Wael W. Mohammed |
| author_facet | Abeer M. Albalahi Akbar Ali Tayyba Zafar Wael W. Mohammed |
| author_sort | Abeer M. Albalahi |
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| description | A bond incident degree (BID) index of a graph G is defined as ∑uv∈EGfdGu,dGv, where dGw denotes the degree of a vertex w of G, EG is the edge set of G, and f is a real-valued symmetric function. The choice fdGu,dGv=adGu+adGv in the aforementioned formula gives the variable sum exdeg index SEIa, where a≠1 is any positive real number. A cut vertex of a graph G is a vertex whose removal results in a graph with more components than G has. A graph of maximum degree at most 4 is known as a molecular graph. Denote by Vn,k the class of all n-vertex graphs with k≥1 cut vertices and containing at least one cycle. Recently, Du and Sun [AIMS Mathematics, vol. 6, pp. 607–622, 2021] characterized the graphs having the maximum value of SEIa from the set Vnk for a>1. In the present paper, we not only characterize the graphs with the minimum value of SEIa from the set Vnk for a>1, but we also solve a more general problem concerning a special type of BID indices. As the obtained extremal graphs are molecular graphs, they remain extremal if one considers the class of all n-vertex molecular graphs with k≥1 cut vertices and containing at least one cycle. |
| format | Article |
| id | doaj-art-e6d69f7ebe6648ddb97cca7528321f0c |
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| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e6d69f7ebe6648ddb97cca7528321f0c2025-08-20T02:21:10ZengWileyDiscrete Dynamics in Nature and Society1607-887X2021-01-01202110.1155/2021/9970254Some Bond Incident Degree Indices of (Molecular) Graphs with Fixed Order and Number of Cut VerticesAbeer M. Albalahi0Akbar Ali1Tayyba Zafar2Wael W. Mohammed3Department of MathematicsDepartment of MathematicsKnowledge Unit of ScienceDepartment of MathematicsA bond incident degree (BID) index of a graph G is defined as ∑uv∈EGfdGu,dGv, where dGw denotes the degree of a vertex w of G, EG is the edge set of G, and f is a real-valued symmetric function. The choice fdGu,dGv=adGu+adGv in the aforementioned formula gives the variable sum exdeg index SEIa, where a≠1 is any positive real number. A cut vertex of a graph G is a vertex whose removal results in a graph with more components than G has. A graph of maximum degree at most 4 is known as a molecular graph. Denote by Vn,k the class of all n-vertex graphs with k≥1 cut vertices and containing at least one cycle. Recently, Du and Sun [AIMS Mathematics, vol. 6, pp. 607–622, 2021] characterized the graphs having the maximum value of SEIa from the set Vnk for a>1. In the present paper, we not only characterize the graphs with the minimum value of SEIa from the set Vnk for a>1, but we also solve a more general problem concerning a special type of BID indices. As the obtained extremal graphs are molecular graphs, they remain extremal if one considers the class of all n-vertex molecular graphs with k≥1 cut vertices and containing at least one cycle.http://dx.doi.org/10.1155/2021/9970254 |
| spellingShingle | Abeer M. Albalahi Akbar Ali Tayyba Zafar Wael W. Mohammed Some Bond Incident Degree Indices of (Molecular) Graphs with Fixed Order and Number of Cut Vertices Discrete Dynamics in Nature and Society |
| title | Some Bond Incident Degree Indices of (Molecular) Graphs with Fixed Order and Number of Cut Vertices |
| title_full | Some Bond Incident Degree Indices of (Molecular) Graphs with Fixed Order and Number of Cut Vertices |
| title_fullStr | Some Bond Incident Degree Indices of (Molecular) Graphs with Fixed Order and Number of Cut Vertices |
| title_full_unstemmed | Some Bond Incident Degree Indices of (Molecular) Graphs with Fixed Order and Number of Cut Vertices |
| title_short | Some Bond Incident Degree Indices of (Molecular) Graphs with Fixed Order and Number of Cut Vertices |
| title_sort | some bond incident degree indices of molecular graphs with fixed order and number of cut vertices |
| url | http://dx.doi.org/10.1155/2021/9970254 |
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