Some Bond Incident Degree Indices of Cactus Graphs
A connected graph in which no edge lies on more than one cycle is called a cactus graph (also known as Husimi tree). 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 symmetri...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/8325139 |
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| author | Akbar Ali Akhlaq Ahmad Bhatti Naveed Iqbal Tariq Alraqad Jaya Percival Mazorodze Hicham Saber Abdulaziz M. Alanazi |
| author_facet | Akbar Ali Akhlaq Ahmad Bhatti Naveed Iqbal Tariq Alraqad Jaya Percival Mazorodze Hicham Saber Abdulaziz M. Alanazi |
| author_sort | Akbar Ali |
| collection | DOAJ |
| description | A connected graph in which no edge lies on more than one cycle is called a cactus graph (also known as Husimi tree). 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. This study involves extremal results of cactus graphs concerning the following type of the BID indices: IfiG=∑uv∈EGfidGu/dGu+fidGv/dGv, where i∈1,2, f1 is a strictly convex function, and f2 is a strictly concave function. More precisely, graphs attaining the minimum and maximum Ifi values are studied in the class of all cactus graphs with a given number of vertices and cycles. The obtained results cover several well-known indices including the general zeroth-order Randić index, multiplicative first and second Zagreb indices, and variable sum exdeg index. |
| format | Article |
| id | doaj-art-4bf9c6b7a4b74596979d8e25f5b3f442 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4bf9c6b7a4b74596979d8e25f5b3f4422025-02-03T01:24:44ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/8325139Some Bond Incident Degree Indices of Cactus GraphsAkbar Ali0Akhlaq Ahmad Bhatti1Naveed Iqbal2Tariq Alraqad3Jaya Percival Mazorodze4Hicham Saber5Abdulaziz M. Alanazi6Department of MathematicsDepartment of Sciences and HumanitiesDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsSchool of MathematicsA connected graph in which no edge lies on more than one cycle is called a cactus graph (also known as Husimi tree). 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. This study involves extremal results of cactus graphs concerning the following type of the BID indices: IfiG=∑uv∈EGfidGu/dGu+fidGv/dGv, where i∈1,2, f1 is a strictly convex function, and f2 is a strictly concave function. More precisely, graphs attaining the minimum and maximum Ifi values are studied in the class of all cactus graphs with a given number of vertices and cycles. The obtained results cover several well-known indices including the general zeroth-order Randić index, multiplicative first and second Zagreb indices, and variable sum exdeg index.http://dx.doi.org/10.1155/2022/8325139 |
| spellingShingle | Akbar Ali Akhlaq Ahmad Bhatti Naveed Iqbal Tariq Alraqad Jaya Percival Mazorodze Hicham Saber Abdulaziz M. Alanazi Some Bond Incident Degree Indices of Cactus Graphs Journal of Mathematics |
| title | Some Bond Incident Degree Indices of Cactus Graphs |
| title_full | Some Bond Incident Degree Indices of Cactus Graphs |
| title_fullStr | Some Bond Incident Degree Indices of Cactus Graphs |
| title_full_unstemmed | Some Bond Incident Degree Indices of Cactus Graphs |
| title_short | Some Bond Incident Degree Indices of Cactus Graphs |
| title_sort | some bond incident degree indices of cactus graphs |
| url | http://dx.doi.org/10.1155/2022/8325139 |
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