Comparing the expressibility of two languages formed using NP-complete graph operators

1991 ◽  
pp. 276-290 ◽  
Author(s):  
Iain A. Stewart
Keyword(s):  
Complete Graph ◽  
Np Complete

COMPUTING THE RUPTURE DEGREE IN COMPOSITE GRAPHS

2010 ◽  
Vol 21 (03) ◽  
pp. 311-319 ◽  
Author(s):  
AYSUN AYTAC ◽  
ZEYNEP NIHAN ODABAS
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
The Other ◽  
Trade Off ◽  
Number Of Components ◽  
Np Complete ◽  
Work Done ◽  
Better Than

The rupture degree of an incomplete connected graph G is defined by [Formula: see text] where w(G - S) is the number of components of G - S and m(G - S) is the order of a largest component of G - S. For the complete graph Kn, rupture degree is defined as 1 - n. This parameter can be used to measure the vulnerability of a graph. Rupture degree can reflect the vulnerability of graphs better than or independent of the other parameters. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. Computing the rupture degree of a graph is NP-complete. In this paper, we give formulas for the rupture degree of composition of some special graphs and we consider the relationships between the rupture degree and other vulnerability parameters.

A note on "Some simplified NP-complete graph problems"

1977 ◽  
Vol 9 (3) ◽  
pp. 24-24 ◽  
Author(s):  
M. S. Krishnamoorthy
Keyword(s):  
Complete Graph ◽  
Graph Problems ◽  
Np Complete

scholarly journals Some simplified NP-complete graph problems

1976 ◽  
Vol 1 (3) ◽  
pp. 237-267 ◽  
Author(s):  
M.R. Garey ◽  
D.S. Johnson ◽  
L. Stockmeyer
Keyword(s):  
Complete Graph ◽  
Graph Problems ◽  
Np Complete

scholarly journals An Average Case NP-complete Graph Colouring Problem

2018 ◽  
Vol 27 (5) ◽  
pp. 808-828 ◽  
Author(s):  
LEONID A. LEVIN ◽  
RAMARATHNAM VENKATESAN
Keyword(s):  
Random Graphs ◽  
Polynomial Time ◽  
Complete Graph ◽  
Graph Colouring ◽  
Worst Case ◽  
Average Case ◽  
Graph Problem ◽  
Complete Problems ◽  
Np Complete ◽  
Np Problems

NP-complete problems should be hard on some instances but those may be extremely rare. On generic instances many such problems, especially related to random graphs, have been proved to be easy. We show the intractability of random instances of a graph colouring problem: this graph problem is hard on average unless all NP problems under all samplable (i.e. generatable in polynomial time) distributions are easy. Worst case reductions use special gadgets and typically map instances into a negligible fraction of possible outputs. Ours must output nearly random graphs and avoid any super-polynomial distortion of probabilities. This poses significant technical difficulties.

Parallel bioinspired algorithms for NP complete graph problems

2009 ◽  
Vol 69 (3) ◽  
pp. 221-229 ◽  
Author(s):  
Israel Marck Martínez-Pérez ◽  
Karl-Heinz Zimmermann
Keyword(s):  
Complete Graph ◽  
Graph Problems ◽  
Np Complete ◽  
Bioinspired Algorithms

A note on "A note on 'Some simplified NP-complete graph problems'"

1978 ◽  
Vol 9 (4) ◽  
pp. 17-17 ◽  
Author(s):  
M. R. Garey ◽  
D. S. Johnson
Keyword(s):  
Complete Graph ◽  
Graph Problems ◽  
Np Complete

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

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