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1 edition of A characterization of graphs with interval two-step graphs found in the catalog.

A characterization of graphs with interval two-step graphs

J. Richard Lundgren

# A characterization of graphs with interval two-step graphs

## by J. Richard Lundgren

Published by Naval Postgraduate School, Available from National Technical Information Service in Monterey, Calif, Springfield, Va .
Written in English

Subjects:
• GRAPHS

One of the intriguing open problems on competition graphs is determining what digraphs have interval competition graphs. In this paper we consider this problem for the class of loopless symmetric digraphs. Here we first consider forbidden subgraph characterizations of graphs with interval two- step graphs. We then characterize a large class of graphs with interval two-step graphs, using the Fulkerson-Gross characterization of interval graphs. Interval graphs, Competition graphs, Step graphs.

Edition Notes

The Physical Object ID Numbers Other titles NPS-MA-93-021. Statement by J. Richard Lundgren, Sarah K. Merz, John S. Maybee, Craig W. Rasmussen Contributions Merz, Sarah K., Maybee, John Stanley, Rasmussen, Craig W., Naval Postgraduate School (U.S.). Dept. of Mathematics Pagination 16 p. : Number of Pages 16 Open Library OL25474990M

The three basic types of graphs you should know are bar graphs, line graphs, and circle graphs (or pie charts). When answering questions related to a graph, you should. Examine the entire graph—notice labels and headings. Focus on the information given. Look for major changes—high points, low points, trends. Do not memorize the graph; refer. Graphs of linear functions may be transformed by shifting the graph up, down, left, or right as well as using stretches, compressions, and reflections. The y-intercept and slope of a line may be used to write the equation of a line. The x-intercept is the point at which the graph .

In this video, we consider a graph that models temperature over time. When a function models a real-world context, we can learn a lot about the content from the function's graph. If you're seeing this message, it means we're having trouble loading external resources on our website. Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the range is the set of possible output values, which are shown on the in mind that if the graph continues beyond the portion of the graph we can see, the domain and.

Short tutorial on editing graphs in SPSS to accompany my book 'Discovering Statistics Using SPSS'. Answers Make a frequency table of each set of data. 1. R regular, W whitening, T tartar control, S sensitive 2. 3. Use the intervals 14–16, 17–19, 20–22, 23–25, and 26– 6. line graph is a graph made by connecting the data points from a set of data. A line graph can be useful inFile Size: KB.

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### A characterization of graphs with interval two-step graphs by J. Richard Lundgren Download PDF EPUB FB2

One of the intriguing open problems on competition graphs is determining what digraphs have interval competition graphs. This problem originated in th Cited by: 5.

A characterization of graphs with interval two-step graphs Dedicated to Professor John Maybee on the occasion of his 65th birthday. Author links open overlay panel d Lundgren Sarah K. Merz John S. Maybee Craig W. RasmussenCited by: 5.

characterization of trees with an interval two-step graph has already been provided, we consider that searching a graph for a forbidden subgraph is not necessarily an easy task. If we can find the maximal cliques of the two- step graph in the original graph easily, we can then use known linear-time.

This work was motivated by a paper of Raychaudhuri and Roberts  where they investigated symmetric digraphs with a loop at each vertex.

Under these assumptions, the competition graph is the square of the underlying graph H without loops. Here we will first consider forbidden subgraph characterizations of graphs with interval two-step graphs.

Second, we will characterize a large class of graphs with interval two-step graphs. Calhoun: The NPS Institutional Archive Faculty and Researcher Publications Faculty and Researcher Publications A Characterization of Graphs With.

The competition graph of a symmetric digraph D is the two-step graph of the underlying graph H of D, denoted S2 (H). The two-step graph is also known as the neighborhood graph, and has been studied recently by Brigham and Dutton and by Boland, Brigham and Dutton.

Approved for public release; distribution is of the intriguing open problems on competition graphs is determining what digraphs have interval competition graphs. In this paper we consider this problem for the class of loopless symmetric digraphs.

In this paper we give a similar characterization on the proper interval graphs using the akin concept of an astral triple. Introduction The class of interval graphs (the intersection graphs of intervals on a line) is one of the best known in the graph theory and has numerous applications in many by: One of the first characterizations of interval graphs, given by Lekkerkerker and Boland (), uses the concept of an asteroidal triple.

In this paper we give a similar characterization on the proper interval graphs using the akin concept of an astral by: Interval graphs are characterized as those graphs whose clique matrices satisfy the consecutive 1's property for columns.

One may apply this characterization to a recognition algorithm for interval graphs G + (V, E) in a two-step process. Booth and Leuker have shown that this step.

The graph thus constructed is called an interval graph. Definition An “interval graph” is the graph showing intersecting intervals on a line. So, we associate a set of intervals E= E1,En on a line with the interval graph G=(V,E), where V= 1,n and two vertices, x and y, are linked by an edge if and only if Ex Ey.

ExampleFile Size: KB. Characteristics of Function ok 7 Septem X is speed (X2) when x, interval. The graph of a function that is decreasing on an interval falls from left to right on that interval.

The given function is increasing/decreasing on the interval {x Types of Graphs Utilized in ABA Cumulative Record •When to use cumulative graph over noncumulative graph –Progress toward a specific goal can be measured in cumulative units •E.g., Number of new words learned, quarters saved –Graph is used as personal feedback •Total progress and relative rate of performance easily detectedFile Size: KB.

Introduction. Graphs are a generalization of trees. Like trees, graphs have nodes and edges. (The nodes are sometimes called vertices, and the edges are sometimes called arcs.) However, graphs are more general than trees: In a graph, a node can have any number of incoming edges (in a tree, the root node cannot have any incoming edges, and the.

By the characterization of interval graphs as AT-free chordal graphs, interval graphs are strongly chordal graphs and hence perfect graphs.

Their complements belong to the class of comparability graphs, and the comparability relations are precisely the interval orders. summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals; and: Standard: B: Description: solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals.

Start Practicing. Types of Graphs: Different Ways to Represent Data Line Graphs • Line graphs are used to display continuous data. • Line graphs can be useful in predicting future events when they show trends over time.

Bar Graphs • Bar graphs are used to display categories of data. • A bar graph is one method of comparing data by using solid. (Andy Kriebel, Stacked Area Cart vs. Line Chart - The Great Debate; Emil Johansson, Character Dialog in the Hobbit: An Unexpected Journey measured) 5. Don't overload the chart.

Adding too much information to a single chart eliminates the advantages of processing data visually; we have to read every element one by one!Author: Angela Zoss. Baseball Bar Graph The school baseball team keeps track of how many runs each player gets.

Use the graph below to answer the questions. Number of Runs Player’s Name (x-axis) Number of runs (y-axis) 0 2 4 6 8 10 12 Mark Tracy Doug Patty Sarah 1. How many runs did Sarah have. How many runs did the player with the most runs have. In this lecture we are going to discuss the Introduction to Graph and its various types such as: 1.

Directed 2. Undirected 3. Self Loop 4. Multi Graph 5. Simple Graph 6. Pseudo Graph. Graphfree is programmed to keep your graph from extending awkwardly beyond the edge of the grid and into the margins.

Usually, that’s helpful. But once in a while you have a graph that just clips the edge of your viewing window, and that clipping effect looks a little bit off.An alternative characterization of chordal graphs, due to Gavril (), involves trees and their subtrees.

From a collection of subtrees of a tree, one can define a subtree graph, which is an intersection graph that has one vertex per subtree and an edge connecting any two subtrees that overlap in one or more nodes of the tree.

Gavril showed that the subtree graphs are exactly the chordal.A graph is simply a drawing of the coordinate plane with points plotted on it. These points all have coordinates (x, y).In the graph of a function, the y-coordinate has the value f (x), meaning the coordinates of the graph of a function are (x, f (x)).The possible values of x are elements of the domain of the function, and the possible values for f (x), or y, are the elements of the range of.