A perfect Italian dominating function on a graph G is a function f:V(G)→{0,1,2} satisfying the condition that for every vertex u with f(u)=0, the total weight of f assigned to the neighbors of u is exactly two. The weight of a perfect Italian dominating function is the sum of the weights of the vertices. The perfect Italian domination number of G, denoted γ Ip (G), is the minimum weight of a perfect Italian dominating function of G. We show that if G is a tree on n≥3 vertices, then γ Ip (G)≤[Formula presented]n, and for each positive integer n≡0(mod5) there exists a tree of order n for which equality holds in the bound.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-11237 |
| Date | 15 May 2019 |
| Creators | Haynes, Teresa W., Henning, Michael A. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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