What is the vertex connectivity of a complete graph?

What is the vertex connectivity of a complete graph?

The connectivity (or vertex connectivity) K(G) of a connected graph G (other than a complete graph) is the minimum number of vertices whose removal disconnects G. When K(G) ≥ k, the graph is said to be k-connected (or k-vertex connected). When we remove a vertex, we must also remove the edges incident to it.

How do you prove the connectivity of a graph?

Given a graph with n vertices, prove that if the degree of each vertex is at least (n−1)/2 then the graph is connected. The distance between two vertices in a graph is the length of the shortest path between them. The diameter of a graph is the distance between the two vertices that are farthest apart.

What are the 5 things a graph needs?

There are five things about graph that need our attention when designing graphs:

• visual structures,
• axes and background,
• scales and tick marks,
• grid lines,
• text.

Is a complete graph a clique?

A complete graph is often called a clique. The size of the largest clique that can be made up of edges and vertices of G is called the clique number of G.

What is clique in undirected graph?

A clique is a subset of vertices of an undirected graph G such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs.

How many cliques are in a complete graph?

from each other). 0-cliques correspond to the empty set (sets of 0 vertices), 1-cliques correspond to vertices, 2-cliques to edges, and 3-cliques to 3-cycles….Clique.

graph family	OEIS	number of cliques
complete bipartite graph	A000290	4, 9, 16, 25, 36, 49, 64, 81, 100.

Is clique problem NP-complete?

In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph. Most versions of the clique problem are hard. The clique decision problem is NP-complete (one of Karp’s 21 NP-complete problems).

How do you prove a problem is NP?

1. To prove your problem is NP-complete, you have to prove that it is in NP and that every problem in NP can be “reduced” to your problem.
2. A problem is “in NP” if, given a potential solution, you can verify that it is correct or incorrect in polynomial time.

Is Hamiltonian path NP complete?

Any Hamiltonian Path can be made into a Hamiltonian Circuit through a polynomial time reduction by simply adding one edge between the first and last point in the path. Therefore we have a reduction, which means that Hamiltonian Paths are in NP Hard, and therefore in NP Complete.

Is 3 clique NP complete?

The main idea is that the structure of 3-SAT is rich enough for the literals/clauses to be interpreted as (groups) of vertices. This then allows us to convert instances of 3-SAT to instances of graph theoretic problems. We will show that CLIQUE is an NP complete problem.

Why is the clique problem in NP?

The Clique Decision Problem belongs to NP-Hard – A problem L belongs to NP-Hard if every NP problem is reducible to L in polynomial time. Thus, if S is reducible to C in polynomial time, every NP problem can be reduced to C in polynomial time, thereby proving C to be NP-Hard.

Is P An NP?

NP-hard problems are those at least as hard as NP problems; i.e., all NP problems can be reduced (in polynomial time) to them. If any NP-complete problem is in P, then it would follow that P = NP. However, many important problems have been shown to be NP-complete, and no fast algorithm for any of them is known.

Are NP-complete problems Decidable?

There are certain NP-Hard problems that also exist in NP. They are decidable, verifiable in polynomial time and are a polynomial reduction of an NP problem. These are said to be NP-Complete. Any NP-complete problem, using a polynomial-time function, can be reduced to SAT.

What is NP problem example?

An example of an NP-hard problem is the decision subset sum problem: given a set of integers, does any non-empty subset of them add up to zero? That is a decision problem and happens to be NP-complete.

Why is halting problem not NP?

– If we had a polynomial time algorithm for the halting problem, then we could solve the satisfiability problem in polynomial time using A and X as input to the algorithm for the halting problem . – Hence the halting problem is an NP-hard problem which is not in NP. – So it is not NP-complete.

Is TSP tractable?

As the only solutions to TSP are intractable, TSP is known as an intractable problem. It hasn’t actually been proven that there is no tractable solution to TSP, although many of the world’s top computer scientists have worked on this problem for the last 40 years, trying to find a solution but without success.

How many subproblems are in TSP at most?

There are at most O(n*2n) subproblems, and each one takes linear time to solve.

Has the traveling salesman problem been solved?

Scientists in Japan have solved a more complex traveling salesman problem than ever before. The previous standard for instant solving was 16 “cities,” and these scientists have used a new kind of processor to solve 22 cities. They say it would have taken a traditional von Neumann CPU 1,200 years to do the same task.

Is Travelling salesman NP-complete?

Traveling Salesman Optimization(TSP-OPT) is a NP-hard problem and Traveling Salesman Search(TSP) is NP-complete. However, TSP-OPT can be reduced to TSP since if TSP can be solved in polynomial time, then so can TSP-OPT(1).

Is NP-hard harder than NP-complete?

An NP-hard problem can be beyond NP. The polynomial-time reduction from your X to any problem in NP does not necessarily have a polynomial-time inverse. If the inverse is harder, then the verification is harder. An NP-complete problem, on the other hand, is one that is NP-hard and itself in NP.

What is harder than NP-complete?

There are complexity classes more “difficult” than NP, for example PSPACE, EXPTIME or EXPSPACE, and all these contain NP-hard but not NP-complete problems. There are also decision problems that are NP-hard but not NP-complete, for example the halting problem.

Is longest common subsequence NP-complete?

The general longest common subsequence problem (LCS) over a binary alphabet is NP-complete.

How do you solve the longest common subsequence problem?

Let X be a sequence of length m and Y a sequence of length n. Check for every subsequence of X whether it is a subsequence of Y, and return the longest common subsequence found. There are 2m subsequences of X. Testing sequences whether or not it is a subsequence of Y takes O(n) time.

How do you find the longest substring between two strings?

Given two strings ‘X’ and ‘Y’, find the length of the longest common substring.

1. Examples :
2. Approach: Let m and n be the lengths of first and second strings respectively. A simple solution is to one by one consider all substrings of first string and for every substring check if it is a substring in second string.

Can there be more than one longest common subsequence?

So a string of length n has 2n-1 different possible subsequences since we do not consider the subsequence with length 0. This implies that the time complexity of the brute force approach will be O(n * 2n). Note that it takes O(n) time to check if a subsequence is common to both the strings.

Is edge connected graph?

In graph theory, a connected graph is k-edge-connected if it remains connected whenever fewer than k edges are removed. The edge-connectivity of a graph is the largest k for which the graph is k-edge-connected.

What is the edge connectivity of a complete graph of V vertices?

The edge-connectivity λ(G) is the size of a smallest edge cut, and the local edge-connectivity λ(u, v) of two vertices u, v is the size of a smallest edge cut disconnecting u from v. Again, local edge-connectivity is symmetric. A graph is called k-edge-connected if its edge connectivity is k or greater.

Is it possible to contract an edge and increase the vertex connectivity of a graph?

From observation of answer of Jukka Kohonen, the following proposition may be correct. Let G is a 2-connected graph and S is its minimal vertex cut. If there are at least two non-trivial connected components of G−S, then contracting any edge of G will not strictly increase the vertex connectivity of G.

What is edge connected?

The minimum number of edges whose deletion from a graph disconnects. , also called the line connectivity. The edge connectivity of a disconnected graph is 0, while that of a connected graph with a graph bridge is 1.

What is the vertex connectivity?

The vertex connectivity of a graph , also called “point connectivity” or simply “connectivity,” is the minimum size of a vertex cut, i.e., a vertex subset such that. is disconnected or has only one vertex.

What is the contraction graph?

The contraction of a pair of vertices and of a graph produces a graph in which the two nodes and are replaced with a single node such that is adjacent to the union of the nodes to which and were originally adjacent.

What is Homeomorphic graph?

graph theory …graphs are said to be homeomorphic if both can be obtained from the same graph by subdivisions of edges. For example, the graphs in Figure 4A and Figure 4B are homeomorphic.

What is a normal contraction pattern?

In a normal labor, one contraction every two to three minutes or less than five contractions in a 10 minute period is ideal. A uterus must rest between contractions, having sufficient uterine resting tone (soft to the touch), and uterine resting time (about one minute).

What does contraction monitor look like?

Contractions are in red. When you’re looking at the screen, the fetal heart rate is usually on the top and the contractions at the bottom. When the machine prints out graph paper, you’ll see the fetal heart rate to the left and the contractions to the right.

How strong do contractions get on monitor?

During normal labor, the amplitude of contractions increases from an average of 30 mm Hg in early labor to 50 mm Hg in later first stage and 50 to 80 mm Hg during the second stage.

What is abnormal CTG?

An abnormal CTG has two or more features which are non-reassuring, or any abnormal features. Further information about classifying FHR traces: If repeated accelerations are present with reduced variability, the FHR trace should be regarded as reassuring.

How do you read a Partogram?

In the cervical dilatation section of the partograph, down the left side, are the numbers 0–10. Each number/square represents 1 cm dilatation. Along the bottom of this section are 24 squares, each representing 1 hour.

What is alert line?

Alert line • A line drawn from the point of cervical dilatation noted at the first vaginal examination in active labour. This line denotes a dilatation rate of 1cm/hour.

What is Action Line in Partogram?

A number of common partogram designs follow the work of Philpott and Castle’ and most incorporate an action line. An action line allows unambiguous diagnosis of prolonged labour, enabling the timing of intervention to be based on the rate of cervical dilatation.

What are the principles of Partograph?

It is based on the following principles: The active phase of labour commences at 3 cm cervical dilatation. The latent phase of labour should last not longer than 8 hours. During active labour, the rate of cervical dilatation should be not slower than 1 cm/hour.

What is the normal Labour?

In 1997, the World Health Organization defined normal birth as “spontaneous in onset, low-risk at the start of labor and remaining so throughout labor and delivery. The infant is born spontaneously in the vertex position between 37 and 42 completed weeks of pregnancy.

What is Labor Monitoring?

Fetal heart monitoring is a way to check the heart rate of your baby (fetus) during labor. The heart rate is a good way to find out if your baby is doing well. It can show if there is a problem. Monitoring may be done all the time during labor (continuous) or at set times (intermittent).

How do you monitor a woman in labor?

Monitor maternal condition by measuring her blood pressure and temperature every 4 hours, and her pulse rate every 30 minutes. Assess the progress of labour by checking uterine contractions (length, strength and frequency) every 30 minutes, descent of the head every two hours and cervical dilatation every four hours.

How do I check my labor status?

Determine if true labour has begun and the stage it has reached, based on measuring the dilatation of the cervix. Assess the progress of labour in terms of the rate of increase in cervical dilatation and the descent of the fetus down the birth canal. Identify the fetal presentation and position.

What are the 4 stages of labor?

There are four stages of labor.

• First stage of labor. Thinning (effacement) and opening (dilation) of the cervix.
• Second stage of labor. Your baby moves through the birth canal.
• Third stage of labor. Afterbirth.
• Fourth stage of labor. Recovery.

What is the first stage of labor?

The first stage of labor and birth occurs when you begin to feel regular contractions, which cause the cervix to open (dilate) and soften, shorten and thin (effacement). This allows the baby to move into the birth canal.

How do you meet emotional needs of a laboring patient?

Ways for the nurse to meet the emotional needs of a laboring client are by respecting contraction time, promoting position changes, offering support, as well as supporting pain management efforts.