منابع مشابه
Total Domination in Partitioned Graphs
We present results on total domination in a partitioned graph G = (V,E). Let γt(G) denote the total dominating number of G. For a partition V1, V2, . . . , Vk, k ≥ 2, of V , let γt(G;Vi) be the cardinality of a smallest subset of V such that every vertex of Vi has a neighbour in it and define the following ft(G;V1, V2, . . . , Vk) = γt(G) + γt(G;V1) + γt(G;V2) + . . .+ γt(G;Vk) ft(G; k) = max{f...
متن کاملDomination in partitioned graphs
Let V1, V2 be a partition of the vertex set in a graph G, and let γi denote the least number of vertices needed in G to dominate Vi. We prove that γ1 + γ2 ≤ 45 |V (G)| for any graph without isolated vertices or edges, and that equality occurs precisely if G consists of disjoint 5-paths and edges between their centers. We also give upper and lower bounds on γ1 + γ2 for graphs with minimum valenc...
متن کاملTotal domination in $K_r$-covered graphs
The inflation $G_{I}$ of a graph $G$ with $n(G)$ vertices and $m(G)$ edges is obtained from $G$ by replacing every vertex of degree $d$ of $G$ by a clique, which is isomorph to the complete graph $K_{d}$, and each edge $(x_{i},x_{j})$ of $G$ is replaced by an edge $(u,v)$ in such a way that $uin X_{i}$, $vin X_{j}$, and two different edges of $G$ are replaced by non-adjacent edges of $G_{I}$. T...
متن کاملNonnegative signed total Roman domination in graphs
Let $G$ be a finite and simple graph with vertex set $V(G)$. A nonnegative signed total Roman dominating function (NNSTRDF) on a graph $G$ is a function $f:V(G)rightarrow{-1, 1, 2}$ satisfying the conditionsthat (i) $sum_{xin N(v)}f(x)ge 0$ for each $vin V(G)$, where $N(v)$ is the open neighborhood of $v$, and (ii) every vertex $u$ for which $f(u...
متن کاملTotal Roman domination subdivision number in graphs
A {em Roman dominating function} on a graph $G$ is a function $f:V(G)rightarrow {0,1,2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A {em total Roman dominating function} is a Roman dominating function with the additional property that the subgraph of $G$ induced by the set of all vertices of positive weight has n...
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: Graphs and Combinatorics
سال: 2009
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-008-0839-z