On Bond Incident Degree Indices of Fixed-Size Bicyclic Graphs with Given Matching Number - Akbar Ali; Abeer M. Albalahi; Abdulaziz M. Alanazi; Akhlaq A. Bhatti; Tariq Alraqad; Hicham Saber; Adel A. Attiya (Mathematics)
A connected graph with p vertices and q edges satisfying <semantics>q=p+1</semantics> is referred to as a bicyclic graph. This paper is concerned with an optimal study of the BID (bond incident degree) indices of fixed-size bicyclic graphs with a given matching number. Here, a BID index of a graph G is the number <semantics>BIDf(G)=∑vw∈E(G)f(dG(v),dG(w))</semantics>, where <semantics>E(G)</semantics> represents G’s edge set, <semantics>dG(v)</semantics> denotes vertex v’s degree, and <semantics>f</semantics> is a real-valued symmetric function defined on the Cartesian square of the set of all different members of G’s degree sequence. Our results cover several existing indices, including the Sombor index and symmetric division deg index.