Connected k-dominating graphs
نویسندگان
چکیده
منابع مشابه
Weighted connected k-domination and weighted k-dominating clique in distance-hereditary graphs
A graph is distance-hereditary if the distance between any two vertices in a connected induced subgraph is the same as in the original graph. This paper presents e-cient algorithms for solving the weighted connected k-domination and the weighted k-dominating clique problems in distance-hereditary graphs. c © 2001 Elsevier Science B.V. All rights reserved.
متن کاملConnected dominating sets on dynamic geometric graphs
We propose algorithms for efficiently maintaining a constant-approximate minimum connected dominating set (MCDS) of a geometric graph under node insertions and deletions. Assuming that two nodes are adjacent in the graph iff they are within a fixed geometric distance, we show that an O(1)-approximate MCDS of a graph in R d with n nodes can be maintained with polylogarithmic (in n) work per node...
متن کاملConnected odd dominating sets in graphs
An odd dominating set of a simple, undirected graph G = (V,E) is a set of vertices D ⊆ V such that |N [v]∩D| ≡ 1 mod 2 for all vertices v ∈ V . It is known that every graph has an odd dominating set. In this paper we consider the concept of connected odd dominating sets. We prove that the problem of deciding if a graph has a connected odd dominating set is NP-complete. We also determine the exi...
متن کامل2-connected Graphs with Small 2-connected Dominating Sets
Let G be a 2-connected graph. A subset D of V (G) is a 2-connected dominating set if every vertex of G has a neighbor in D and D induces a 2-connected subgraph. Let γ2(G) denote the minimum size of a 2-connected dominating set of G. Let δ(G) be the minimum degree of G. For an n-vertex graph G, we prove that γ2(G) ≤ n ln δ(G) δ(G) (1 + oδ(1)) where oδ(1) denotes a function that tends to 0 as δ →...
متن کاملThe k-dominating cycles in graphs
For a graph G, let σ̄k+3(G) = min {d(x1) + d(x2) + · · · + d(xk+3) − |N(x1) ∩ N(x2) ∩ · · · ∩ N(xk+3)| | x1, x2, · · · , xk+3 are k + 3 independent vertices in G}. In [5], H. Li proved that if G is a 3-connected graph of order n and σ̄4(G) ≥ n+3, then G has a maximum cycle such that each component of G−C has at most one vertex. In this paper, we extend this result as follows. Let G be a (k + 2)-c...
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 Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2018.09.006