[HTML][HTML] On unicyclic graphs with a given number of pendent vertices or matching number and their graphical edge-weight-function indices

A Ali, AM Alanazi, TS Hassan, Y Shang - Mathematics, 2024 - mdpi.com
Consider a unicyclic graph G with edge set E (G). Let f be a real-valued symmetric function
defined on the Cartesian square of the set of all distinct elements of G's degree sequence. A …

[PDF][PDF] On Bond Incident Degree Indices of Fixed-Size Bicyclic Graphs with Given Matching Number.

A Ali, AM Albalahi, AM Alanazi, AA Bhatti… - Mathematics (2227 …, 2024 - researchgate.net
A connected graph with p vertices and q edges satisfying q= p+ 1 is referred to as a bicyclic
graph. This paper is concerned with an optimal study of the BID (bond incident degree) …

On a Conjecture Concerning the Complementary Second Zagreb Index

H Saber, T Alraqad, A Ali, AM Alanazi… - arXiv preprint arXiv …, 2025 - arxiv.org
The complementary second Zagreb index of a graph $ G $ is defined as $ cM_2 (G)=\sum_
{uv\in E (G)}|(d_u (G))^ 2-(d_v (G))^ 2| $, where $ d_u (G) $ denotes the degree of a vertex …