Weighted domination number of cactus graphs

TL;DR

This paper presents a linear-time algorithm based on DFS for computing the weighted domination number of vertex-weighted cactus graphs, optimizing computational efficiency.

Contribution

It introduces a novel linear algorithm leveraging DFS for calculating the weighted domination number specifically in cactus graphs.

Findings

Algorithm requires less than 12n+5b additions and 9n+2b min-operations

Efficient computation for weighted domination in cactus graphs

Applicable to large graphs with optimized performance

Abstract

In the paper, we write a linear algorithm for calculating the weighted domination number of a vertex-weighted cactus. The algorithm is based on the well known depth first search (DFS) structure. Our algorithm needs less than $12n+5b$ additions and $9n+2b$ $\min$-operations where $n$ is the number of vertices and $b$ is the number of blocks in the cactus.