The signed domatic number of some regular graphs
نویسندگان
چکیده
منابع مشابه
The signed domatic number of some regular graphs
Let G be a finite and simple graph with vertex set V (G), and let f : V (G) → {−1, 1} be a two-valued function. If ∑ x∈N[v] f (x) ≥ 1 for each v ∈ V (G), where N[v] is the closed neighborhood of v, then f is a signed dominating function on G. A set {f1, f2, . . . , fd} of signed dominating functions on Gwith the property that ∑d i=1 fi(x) ≤ 1 for each x ∈ V (G), is called a signed dominating fa...
متن کاملThe Domatic Number of Regular Graphs
The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular graph is almost surely at most r, and that for 3-regular random graphs, the domatic number is almost surely equal to 3. We also give a lower bound on the domatic number of a graph in terms of order, minimum degree and m...
متن کاملThe domatic number of regular and almost regular graphs
The domatic number of a graph G, denoted dom(G), is the maximum possible cardinality of a family of disjoint sets of vertices of G, each set being a dominating set of G. It is well known that every graph without isolated vertices has dom(G) ≥ 2. For every k, it is known that there are graphs with minimum degree at least k and with dom(G) = 2. In this paper we prove that this is not the case if ...
متن کاملon the total domatic number of regular graphs
a set $s$ of vertices of a graph $g=(v,e)$ without isolated vertex is a {em total dominating set} if every vertex of $v(g)$ is adjacent to some vertex in $s$. the {em total domatic number} of a graph $g$ is the maximum number of total dominating sets into which the vertex set of $g$ can be partitioned. we show that the total domatic number of a random $r$-regular graph is almost...
متن کاملSigned k-domatic numbers of graphs
Let D be a finite and simple digraph with vertex set V (D), and let f : V (D)→ {−1,1} be a two-valued function. If k ≥ 1 is an integer and ∑x∈N−[v] f (x) ≥ k for each v∈V (D), where N−[v] consists of v and all vertices of D from which arcs go into v, then f is a signed k-dominating function on D. A set { f1, f2, . . . , fd} of distinct signed k-dominating functions of D with the property that ∑...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2008.11.012