Seminar on Theoretical Computer Science

On Monday, February 15, 2021, 15:00 hours, Antoaneta Klobučar (J. J. Strossmayer University of Osijek, Faculty of Economics in Osijek) will give lecture Properties of double Roman domination on cardinal products of graphs within Seminar on Theoretical Computer Science.

Lecture will be held via Zoom application:

Link: https://zoom.us/j/92408753786?pwd=dGtCRTNTRVVoSStXYjlvb3lJckplUT09

Meeting ID: 924 0875 3786

Passcode: 184576

Abstract:

Double Roman domination is a stronger version of Roman domination that doubles the protection. The areas now have 0, 1, 2 or 3 legions. Every attacked area needs 2 legions for its defence, either their own, or borrowed from 1 or 2 neighbouring areas, which still have to keep at least 1 legion to themselves. The minimal number of legions in all areas together is equal to the double Roman domination number.

In this paper we determine an upper bound and a lower bound for double Roman domination numbers on cardinal product of any two graphs. Also we determine the exact values of double Roman domination numbers on P₂ × G (for many types of graph G). Also, the double Roman domination number is found for P₂ × P_n, P₃ × P_n, P₄ × P_n, while upper and lower bounds are given for P₅ × P_n and P₆ × P_n.

Finally, we will give a case study to determine the efficiency of double protection. We will compare double Roman domination versus Roman domination by running a simulation of a battle.

All seminar members and interested audience are invited!