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Is cycle and circuit in graph theory same?
No its not. A cycle is closed trail
What graph has a finite or limited number of data points is?
A discrete graph.
What type of graph uses an X above a number line to represent each number in a set of data?
This graph is called the x graph.
What is the x intercept on a graph?
It is found on the horizontal x axis number line on a graph whereas the y intercept is found on the vertical number line on a graph.
What is a typical number on a graph?
42
What is the chromatic number of an n-vertex simple connected graph which does?
2
What is the chromatic number of an n-vertex simple connected graph which does not contain any odd length cycle. Assume n - 2?
χ(Kn) = n colors
What is the cycle size of the given graph?
The cycle size of a graph is the number of vertices in the smallest cycle in the graph.
Is colour-critical graph always connected?
Yes. If it was disconnected, you could remove an edge from the component with the lower chromatic number. This wouldn't affect the chromatic number of the first component.
What has the author Barry Graham written?
Barry Graham has written: 'An algorithm to determine the chromatic number of a graph' 'Get out as early as you can' 'Before: A Novel'
How do you find the chromatic number?
There are many ways to find the chromatic number. One way is to write the chromatic polynomial and obtain it from that. For example, let's look at a complete graph on 3 points which looks like a triangle. We can color the first vertex in x ways, the second is x-1 ways and the third in x-2 ways. So the chromatic polynomial is C(x)=x(x-1)(x-2) not the smallest natural number, N, such that C(N) is not equal to zero is the chromatic number. So in this case it is 3. This number tells us the we can color the graph with 3 different colors and have no vertices with the same color. Any smaller number of colors, say 2 would not work.So the answer is find C(x) the chromatic polynomial and then find the smallest natural number such that C(x) is not zero. There are many other methods to find it, but that one is sometimes the simplest.
What is a negative cycle in Graph?
In a weighed graph, a negative cycle is a cycle whose sum of edge weights is negative
What is index on a graph?
In graph theory, an index on a graph typically refers to a numerical value representing certain properties of the graph or its vertices. For instance, the degree index counts the number of edges connected to a vertex, while the chromatic index indicates the minimum number of colors needed to color the edges of a graph without adjacent edges sharing the same color. These indices help in analyzing and understanding the structure and behavior of graphs in various applications.
What is the United State's chromatic number?
4
What is the chromatic polynomial of Peterson graph?
The chromatic polynomial for the Petersen (not Peterson) graph ispi(z) = (z - 2)* (z - 1)*z*(z^7 - 12*z^6 + 67*z^5 - 230*z^4 + 529*z^3 - 814*z^2 + 775*z - 352).
Is cycle and circuit in graph theory same?
No its not. A cycle is closed trail
How does the concept of a vertex cover relate to the existence of a Hamiltonian cycle in a graph?
In graph theory, a vertex cover is a set of vertices that covers all edges in a graph. The concept of a vertex cover is related to the existence of a Hamiltonian cycle in a graph because if a graph has a Hamiltonian cycle, then its vertex cover must include at least two vertices from each edge in the cycle. This is because a Hamiltonian cycle visits each vertex exactly once, so the vertices in the cycle must be covered by the vertex cover. Conversely, if a graph has a vertex cover that includes at least two vertices from each edge, it may indicate the potential existence of a Hamiltonian cycle in the graph.
