Fault-Tolerant Resolvability in Some Classes of Line Graphs
نویسندگان
چکیده
منابع مشابه
Realizability of Fault Tolerant Graphs∗
A connected graph G is optimal-κ if the connectivity κ(G) = δ(G), where δ(G) is the minimum degree of G. It is super-κ if every minimum vertex cut isolates a vertex. An optimal-κ graph G is moptimal-κ if for any vertex set S ⊆ V (G) with |S| ≤ m, G−S is still optimal-κ. The maximum integer of such m, denoted by Oκ(G), is the vertex fault tolerance of G with respect to the property of optimal-κ....
متن کامل4-Prime cordiality of some classes of graphs
Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....
متن کاملFault-Tolerant Graphs for Tori
Motivated by the design of fault-tolerant multiprocessor interconnection networks, this paper considers the following problem: Given a positive integer t and a graph H , construct a graph G from H by adding a minimum number D( t , H ) of edges such that even after deleting any t edges from G the remaining graph contains H as a subgraph. We estimate D( t , H ) for the torus, which is well known ...
متن کاملFault-Tolerant Ring Embedding in Star Graphs
In this paper, we consider an injured star graph with some faulty links and nodes. We show that even with fe n 3 faulty links a Hamiltonian cycle still can be found in an nstar, and that with fv n 3 faulty nodes a ring containing at most 4fv nodes less than that in a Hamiltonian cycle can be found (i.e., containing at leastn! 4fv nodes). In general, in an n-star with fe faulty links and fv faul...
متن کاملApproximating Fault-Tolerant Domination in General Graphs
In this paper we study the NP-complete problem of finding small k-dominating sets in general graphs, which allow k−1 nodes to fail and still dominate the graph. The classic minimum dominating set problem is a special case with k = 1. We show that the approach of having at least k dominating nodes in the neighborhood of every node is not optimal. For each α > 1 it can give solutions k α times la...
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: Mathematical Problems in Engineering
سال: 2020
ISSN: 1024-123X,1563-5147
DOI: 10.1155/2020/1436872