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A trivial graph is a graph with 0 or 1 vertices. [16] A graph with 0 vertices is also called null graph. Turán 1. Pál Turán 2. A Turán graph is a balanced complete multipartite graph. 3. Turán's theorem states that Turán graphs have the maximum number of edges among all clique-free graphs of a given order. 4.
A zero-crossing in a line graph of a waveform representing voltage over time. A zero-crossing is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis (zero value) in the graph of the function.
If P < 0 and D < 0 then all four roots are real and distinct. If P > 0 or D > 0 then there are two pairs of non-real complex conjugate roots. [13] If ∆ = 0 then (and only then) the polynomial has a multiple root. Here are the different cases that can occur: If P < 0 and D < 0 and ∆ 0 ≠ 0, there are a real double root and two real simple ...
The negative values are associated with the poorly connected vertex 6, and the neighbouring articulation point, vertex 4; while the positive values are associated with the other vertices. The signs of the values in the Fiedler vector can therefore be used to partition this graph into two components: { 1 , 2 , 3 , 5 } , { 4 , 6 } {\textstyle \{1 ...
The method also uses a simplified method for finding the term linear in frequency based upon summing the RC-products for each capacitor in the circuit, where the resistor R for a selected capacitor is the resistance found by inserting a test source at its site and setting all other capacitors to zero. Hence the name zero-value time constant ...
A graph with a zero-weight cycle. A related problem is to decide whether the graph has a negative cycle, a cycle in which the sum of weights is less than 0. This related problem can be solved in polynomial time using the Bellman–Ford algorithm. If there is no negative cycle, then the distances found by the Bellman–Ford algorithm can be used ...
The mutual information (MI) of the random variables X and Y is the expected value of the PMI (over all possible outcomes). The measure is symmetric ( (;) = (;)). It can take positive or negative values, but is zero if X and Y are independent. Note that even though PMI may be negative or positive, its expected outcome over all joint ...
If a first-order graph property has probability tending to one on random graphs, then it is possible to list all the -vertex graphs that model the property, with polynomial delay (as a function of ) per graph. [4] A similar analysis can be performed for non-uniform random graphs, where the probability of including an edge is a function of the ...