A two-valued function f defined on the vertices of a graph G (V, E), I : V -+ {-I, I}, is a signed dominating function if the sum of its function values over any closed neighborhood is at least one.Expand

A two-valued function f defined on the vertices of a graph G = (V, E) is a majority dominating function if the sum of its function values over at least half the closed neighborhoods is at least one.Expand

In this note, we establish the exact value of the bipartite Ramsey number b ( P m , K l , n ) for all integers m , n ⩾ 2, where P m denotes a path on m vertices.Expand

ABSTRACT Graph products of circulants are studied. It is shown that if G and H are circulants and gcd(v(G), v(H)) = 1, then every B-product of G and H is again a circulant. We prove that if m ≠ 2,… Expand

Let G = (V, E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex in V is adjacent to a vertex in S and every vertex of V −S is adjacent to a vertex in V −S. The total… Expand

Let n ≥ 1 be an integer and let G be a graph. A set D of vertices in G is defined to be an n-dominating set of G if every vertex of G is within distance n from some vertex of D. The minimum… Expand

We define a simple mechanism which explains why this inequality chain exists and how it is possible to define many similar chains of potentially arbitrary length.Expand