DEGREE-STATUS CONNECTIVITY INDICES: STRUCTURAL PROPERTIES AND QSPR APPLICATIONS TO BENZENOID HYDROCARBONS
Jalappa, Vijendra. N, Boregowda H. S.
Department of Studies and Research in Mathematics,
Tumkur University,Tumkur-572103, Karnataka, India
Abstract: In this work, we introduce two new connectivity indices for a graph G, referred to as the first- and second-degree status connectivity indices. These indices are defined as follows: PS₁(G) is equal to the sum over all edges {s, t} in the graph G of the expression “[σ(s) plus σ(t)] multiplied by (degree of s times degree of t)”; and PS₂(G) is equal to the sum over all edges {s, t} in the graph G of the expression “[σ(s) times σ(t)] multiplied by (degree of s times degree of t)”; where E(G) denotes the edge set of the graph and d(s) denotes degree of a vertex s. These indices have been evaluated for some standard class of graphs. Additionally, certain bounds were investigated. We further investigated the applicability of these indices in modeling the physicochemical properties of benzenoid hydrocarbons. Specifically, this study examines the predictive potential of the indices PS₁(G) and PS₂(G) through cubic regression modeling for benzenoid hydrocarbons. The results indicate that PS₁(G) serves as a more effective predictive index compared to PS₂(G) among the two newly introduced indices. Furthermore, a comparison between the actual and predicted physicochemical properties has been presented for both indices to provide clearer insights.
Keywords: Status, Status connectivity index, Zagreb index, Second status connectivity index.
AMSC:05C07; 05C09; 05C92
VOLUME 9 ISSUE 11 2025: 76 – 88