A Roman Domination Chain

作者：Chellali Mustapha^*; Haynes Teresa W; Hedetniemi Sandra M; Hedetniemi Stephen T; McRae Alice A

来源：Graphs and Combinatorics, 2016, 32(1): 79-92.

DOI：10.1007/s00373-015-1566-x

• Roman domination
• Roman independence
• Roman irredundance
• Roman parameters

For a graph , a Roman dominating function has the property that every vertex with has a neighbor with . The weight of a Roman dominating function is the sum , and the minimum weight of a Roman dominating function on is the Roman domination number of . In this paper, we define the Roman independence number, the upper Roman domination number and the upper and lower Roman irredundance numbers, and then develop a Roman domination chain parallel to the well-known domination chain. We also develop sharpness, strictness and bounds for the Roman domination chain inequalities.

• 出版日期2016-1