Downhill Domination in Graphs

Open access


A path π = (v1, v2, . . . , vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi) ≥ deg(vi+1), where deg(vi) denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] T.W. Haynes S.T. Hedetniemi J. Jamieson and W. Jamieson Downhill and uphill domination in graphs submitted for publication (2013).

  • [2] P. Hall On representation of subsets J. London Math. Soc. 10 (1935) 26-30.

  • [3] T.W. Haynes S.T. Hedetniemi and P.J. Slater Fundamentals of Domination in Graphs (Marcel Dekker 1998).

  • [4] J.D. Hedetniemi S.M. Hedetniemi S.T. Hedetniemi and T. Lewis Analyzing graphs by degrees AKCE Int. J. Graphs Comb. to appear.

  • [5] O. Ore Theory of Graphs (Amer. Math. Soc. Colloq. Publ. 38 1962).

Journal information
Impact Factor

IMPACT FACTOR 2018: 0.741
5-year IMPACT FACTOR: 0.611

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.763
Source Normalized Impact per Paper (SNIP) 2018: 0.934

Mathematical Citation Quotient (MCQ) 2018: 0.42

Target audience:

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 321 197 4
PDF Downloads 110 75 5