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1. • Simple graph possessing no chords

     • A chordless graph is a simple graph possessing no chords. A chordal graph (which possesses no chordless cycles) is not the same as (or converse of) a chordless graph (which possesses no chords).
     mathworld.wolfram.com/ChordlessGraph.html

     Chordless Graph -- from Wolfram MathWorld

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   What is a chordless graph cycle?

   • A graph cycle possessing no chord (sometimes with the added restriction that the cycle be of length four or greater; e.g., West 2000, p. 225), is said to be a chordless cycle . Chordless cycles are important in the study and characterization of perfect graphs .

   Cycle Chord -- from Wolfram MathWorld

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   Is a graph bridge a chord?

   • Graph bridges are not chords since they do not lie on a cycle. Similarly, in order to lie on a cycle, both endpoints of a chord must be of vertex degree at least 3. A graph cycle possessing no chord (sometimes with the added restriction that the cycle be of length four or greater; e.g., West 2000, p. 225), is said to be a chordless cycle .

   Cycle Chord -- from Wolfram MathWorld

   mathworld.wolfram.com/CycleChord.html

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   What is an example of a chord in a graph?

   • For example, in the diamond graph as labeled above, the edge (3,4) is a chord of the cycle (1,3,2,4,1). The motivation for the term "chord" is geometric. In particular, if a cycle is drawn with its vertices lying on the a circle and its chords are drawn as line segments, then the chords of the cycle are chords of the circle (West 2000, p. 225).

   Cycle Chord -- from Wolfram MathWorld

   mathworld.wolfram.com/CycleChord.html

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   What is a chord in a graph cycle?

   • A chord of a graph cycle C is an edge not in the edge set of C whose endpoints lie in the vertex set C (West 2000, p. 225). For example, in the diamond graph as labeled above, the edge (3,4) is a chord of the cycle (1,3,2,4,1). The motivation for the term "chord" is geometric.

   Cycle Chord -- from Wolfram MathWorld

   mathworld.wolfram.com/CycleChord.html

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   What is a chordal graph?

   • A chordal graph, a special type of perfect graph, has no holes of any size greater than three. The girth of a graph is the length of its shortest cycle; this cycle is necessarily chordless. Cages are defined as the smallest regular graphs with given combinations of degree and girth.

   Cycle (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Cycle_(graph_theory)

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   Which graph is chordless but not chordal?

   • For example, the square graph is chordless but not chordal , the diamond graph and tetrahedral graph are chordal but not chordless, and empty graphs , path graphs , and the triangle graph are both chordal and chordless. The numbers of connected simple chordless graphs on , 2, ... nodes are 1, 1, 2, 4, 10, 27, ...

   Chordless Graph -- from Wolfram MathWorld

   mathworld.wolfram.com/ChordlessGraph.html

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4. mathworld.wolfram.com › ChordlessGraphChordless Graph -- from Wolfram MathWorld

   mathworld.wolfram.com › ChordlessGraph

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   Oct 24, 2024 · A chordless graph is a simple graph possessing no chords. A chordal graph (which possesses no chordless cycles) is not the same as (or converse of) a chordless graph (which possesses no chords).

   • Chordless Cycle

     A chordless cycle of a graph is a graph cycle in that has no...

   • Cycle Chord

     A graph cycle possessing no chord (sometimes with the added...

5. en.wikipedia.org › wiki › Cycle_(graph_theory)Cycle (graph theory) - Wikipedia

   en.wikipedia.org › wiki › Cycle_(graph_theory)

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   A chordless cycle in a graph, also called a hole or an induced cycle, is a cycle such that no two vertices of the cycle are connected by an edge that does not itself belong to the cycle. An antihole is the complement of a graph hole.

6. Videos

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     Definition of Chords in Cycles | Graph Theory, Chordless Cycles

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     What is a Graph? | Graph Theory

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     Basic Graph Theory I - vertices, edges, loops, and equivalent graphs

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7. www.youtube.com › watchDefinition of Chords in Cycles | Graph Theory, Chordless ...

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   What is a chord of a cycle in graph theory? We will define chords and give examples in today's graph theory lesson!A chord of a cycle C is an edge that doesn...

   • Video Duration: 5 min
   • Views: 3.3K

   • Author: Wrath of Math

8. mathworld.wolfram.com › ChordlessCycleChordless Cycle -- from Wolfram MathWorld

   mathworld.wolfram.com › ChordlessCycle

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   A chordless cycle of a graph is a graph cycle in that has no cycle chord. Unfortunately, there are conflicting conventions on whether or not 3-cycles should be considered chordless.

9. en.wikipedia.org › wiki › Chordal_graphChordal graph - Wikipedia

   en.wikipedia.org › wiki › Chordal_graph

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   In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have exactly three vertices.

10. www.stat.berkeley.edu › graphnotesUndirected Graphical Models: Chordal Graphs, Decomposable ...

    www.stat.berkeley.edu › graphnotes

    A graph is chordal (also called triangulated) if it contains no chordless cycles of length greater than 3. A graph is complete if E contains all pairs of distinct elements of V.

11. mathworld.wolfram.com › CycleChordCycle Chord -- from Wolfram MathWorld

    mathworld.wolfram.com › CycleChord

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    5 days ago · A graph cycle possessing no chord (sometimes with the added restriction that the cycle be of length four or greater; e.g., West 2000, p. 225), is said to be a chordless cycle. Chordless cycles are important in the study and characterization of perfect graphs.