21,838 research outputs found
On the Independent Domination Number of Regular Graphs
A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. In this paper, we consider questions about independent domination in regular graphs
Discrepancy and Signed Domination in Graphs and Hypergraphs
For a graph G, a signed domination function of G is a two-colouring of the
vertices of G with colours +1 and -1 such that the closed neighbourhood of
every vertex contains more +1's than -1's. This concept is closely related to
combinatorial discrepancy theory as shown by Fueredi and Mubayi [J. Combin.
Theory, Ser. B 76 (1999) 223-239]. The signed domination number of G is the
minimum of the sum of colours for all vertices, taken over all signed
domination functions of G. In this paper, we present new upper and lower bounds
for the signed domination number. These new bounds improve a number of known
results.Comment: 12 page
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