Some Characterizations of Total Outer-connected Domination in Graphs

This research related to total outer-connected dominance regarding graphs aids in revealing significant insights. Theoretical analysis establishes connections with tree-like structures, emphasizing the relationship with outer planarity. Effective algorithms, integrating the linear-time algorithm for trees and the genetic algorithm for general graphs, show effectiveness in locating minimal total outer-connected dominating sets. Practical implications aid in enlightening applications in wireless sensor networks, social networks, and network design, focusing on the benefits of defect tolerance and information dissemination. This research study aids in contributing towards the increased level of understanding, delivering the practical algorithms, suggesting real- world applications, and providing guidance to future research directions for total outer-connected dominance within the graph.