On the Toughness of Graphs
نویسنده
چکیده
The toughness of a graph is the graph’s vulnerability to having vertices removed. For example, if vertices of the graph represent homes, and the edge of the graph represent telephone lines connecting them, then the toughness measures how badly telephone communication can broken down by relatively few lightening strikes. In this paper the maximum networks are obtained with prescribed order and toughness. Mathematics Subject Classification: 05C40
منابع مشابه
Normalized Tenacity and Normalized Toughness of Graphs
In this paper, we introduce the novel parameters indicating Normalized Tenacity ($T_N$) and Normalized Toughness ($t_N$) by a modification on existing Tenacity and Toughness parameters. Using these new parameters enables the graphs with different orders be comparable with each other regarding their vulnerabilities. These parameters are reviewed and discussed for some special graphs as well.
متن کاملToughness of the Networks with Maximum Connectivity
The stability of a communication network composed of processing nodes and communication links is of prime importance to network designers. As the network begins losing links or nodes, eventually there is a loss in its effectiveness. Thus, communication networks must be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible...
متن کاملOn the tenacity of cycle permutation graph
A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.
متن کاملOn Toughness and Hamiltonicity of 2K2-Free Graphs
The toughness of a (non-complete) graph G is the minimum value of t for which there is a vertex cut A whose removal yields |A|/t components. Determining toughness is an NP-hard problem for general input graphs. The toughness conjecture of Chvátal, which states that there exists a constant t such that every graph on at least 3 vertices with toughness at least t is hamiltonian, is still open for ...
متن کاملA Survey on Complexity of Integrity Parameter
Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including toughness, binding number, rate of disruption, neighbor-connectivity, integrity, mean integrity, edgeconnectivity vector, l-connectivity and tenacity. In this paper we discuss Integrity and its properties in vulnerability calculation. The integrity of a graph G, I(G), is defined t...
متن کاملA note on the approximability of the toughness of graphs
We show that, if NP 6= ZPP, for any ε > 0, the toughness of a graph with n vertices is not approximable in polynomial time within a factor of 1 2 (n 2 ). We give a 4-approximation for graphs with toughness bounded by 1 3 and we show that this result cannot be generalized to graphs with a bounded toughness. More exactly we prove that there is no constant approximation for graphs with bounded tou...
متن کامل