Graph-Theoretic Insights into Birth Rate Trends: Exploring Platt Number in Constructed Signed Network

The definition of a signed graph is
$\Sigma(\mathrm{W},\sigma)$
, where W = (V,E) denotes a base graph with its set of edges (E) and vertices (V). The function σ, known as the signature or sign mapping, assigns a sign (+ or -) from the sign group {+, -} to each edge in E. The purpose of this study is to determine the upper limits of Platt numbers for signed star, butterfly, and bull graphs. Furthermore, Character points (CP) from a friendship or judgment matrix are analysed using a signed graph to identify patterns in birth rates between districts and years. Higher CP districts indicate potential expansion, whereas lower CP districts may see relative drops in birth rates. Insights into district contributions to birth rate trends can be gained by analysing positive and negative centralities, which can help direct targeted measures for socioeconomic equity and sustainable development.