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An indifference graph, formed from a set of points on the real line by connecting pairs of points whose distance is at most one. In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting two vertices by an edge when their numbers are within one unit of each other. [1]
(The RR interval will shorten when the heart speeds up, and lengthen when it slows.) An RR tachograph is a graph of the numerical value of the RR-interval versus time. In the context of RR tachography , a Poincaré plot is a graph of RR( n ) on the x -axis versus RR( n + 1) (the succeeding RR interval) on the y -axis, i.e. one takes a sequence ...
An interval graph is an undirected graph G formed from a family of intervals , =,,, … by creating one vertex v i for each interval S i, and connecting two vertices v i and v j by an edge whenever the corresponding two sets have a nonempty intersection.
Let N be the set of all interval colourable graphs. For a graph G ∈ N, the least and the greatest values of t for which G has an interval t-colouring are denoted by w(G) and W(G), respectively. An interval edge coloring of a graph is said to be equitable interval edge coloring if any two color classes of a graph differ by at most one.
In this same graph, the maximal cliques are the sets {a, b} and {b, c}. A MIS is also a dominating set in the graph, and every dominating set that is independent must be maximal independent, so MISs are also called independent dominating sets. The top two P 3 graphs are maximal independent sets while the bottom two are independent sets, but not ...
It is interesting about interval chromatic number that it is easily computable. Indeed, by a simple greedy algorithm one can efficiently find an optimal partition of the vertex set of H into X < (H) independent intervals. This is in sharp contrast with the fact that even the approximation of the usual chromatic number of graph is an NP hard task.
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The edges of the graph are d-tuples of intervals, one interval in every real line. [1] The simplest case is d = 1. The vertex set of a 1-interval hypergraph is the set of real numbers; each edge in such a hypergraph is an interval of the real line. For example, the set { [−2, −1], [0, 5], [3, 7] } defines a 1-interval