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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Published inJournal of mathematics (Hidawi) Vol. 2022; no. 1
Main Authors Ali, Akbar, Bhatti, Akhlaq Ahmad, Iqbal, Naveed, Alraqad, Tariq, Mazorodze, Jaya Percival, Saber, Hicham, Alanazi, Abdulaziz M.
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 01.01.2022
Hindawi Limited
Subjects
Apexes
Graphs
Mathematics
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Summary: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/8325139