On the independence and domination numbers of replacement product graphs
نویسندگان
چکیده
منابع مشابه
A note on domination and independence-domination numbers of graphs∗
Vizing’s conjecture is true for graphs G satisfying γ(G) = γ(G), where γ(G) is the domination number of a graph G and γ(G) is the independence-domination number of G, that is, the maximum, over all independent sets I in G, of the minimum number of vertices needed to dominate I . The equality γ(G) = γ(G) is known to hold for all chordal graphs and for chordless cycles of length 0 (mod 3). We pro...
متن کاملDomination and independence subdivision numbers of graphs
The domination subdivision number sdγ(G) of a graph is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number. Arumugam showed that this number is at most three for any tree, and conjectured that the upper bound of three holds for any graph. Although we do not prove this interesting conjecture, we give an upp...
متن کاملOn average lower independence and domination numbers in graphs
Theaverage lower independencenumber iav(G)of a graphG=(V ,E) is defined as 1 |V | ∑ v∈V iv(G), and the average lower domination number av(G) is defined as 1 |V | ∑ v∈V v(G), where iv(G) (resp. v(G)) is the minimum cardinality of a maximal independent set (resp. dominating set) that contains v.We give an upper bound of iav(G) and av(G) for arbitrary graphs. Then we characterize the graphs achiev...
متن کاملThe minus k-domination numbers in graphs
For any integer , a minus k-dominating function is afunction f : V (G) {-1,0, 1} satisfying w) for every vertex v, where N(v) ={u V(G) | uv E(G)} and N[v] =N(v)cup {v}. The minimum of the values of v), taken over all minusk-dominating functions f, is called the minus k-dominationnumber and is denoted by $gamma_k^-(G)$ . In this paper, we introduce the study of minu...
متن کاملDouble Roman domination and domatic numbers of graphs
A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in cite{bhh} as a function$f:V(G)rightarrow{0,1,2,3}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least twoneighbors assigned 2 under $f$ or one neighbor $w$ with $f(w)=3$, and if $f(v)=1$, then the vertex $v$ must haveat least one neighbor $u$ with $f(u)ge 2$. The weight of a double R...
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: Involve, a Journal of Mathematics
سال: 2016
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2016.9.181