Monophonic domination in special graph structures and related properties

摘要

In this paper, we study the monophonic domination number of specialgraph structures like k -Dimensional Cube Qk, triangle-free Graphs,Tree, Middle Graphs and Edge Deleted Graphs. Certain general propertiessatisfied by the monophonic domination number are discussed. Italso, realizes the existence of monophonic domination number of G interms of monophonic diameter and girth. Finally, we study how themonophonic domination number is affected when one or more edges aredeleted from a complete graph Kp.