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The friendship graphs F 2, F 3 and F 4. In the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) F n is a planar, undirected graph with 2n + 1 vertices and 3n edges. [1] The friendship graph F n can be constructed by joining n copies of the cycle graph C 3 with a common vertex, which becomes a universal ...
The Shaw graph, the first known Harris graph, is of order 9 and size 14, discovered by Douglas Shaw. In graph theory , a Harris graph is defined as an Eulerian , tough , non- Hamiltonian graph . [ 1 ] [ 2 ] Harris graphs were introduced in 2013 when, at the University of Michigan , Harris Spungen conjectured that a tough , Eulerian graph would ...
This graph has circuit rank r = 2 because it can be made into a tree by removing two edges, for instance the edges 1–2 and 2–3, but removing any one edge leaves a cycle in the graph. In graph theory, a branch of mathematics, the circuit rank, cyclomatic number, cycle rank, or nullity of an undirected graph is the minimum number of edges ...
Graph Theory, 1736–1936 is a book in the history of mathematics on graph theory. It focuses on the foundational documents of the field, beginning with the 1736 paper of Leonhard Euler on the Seven Bridges of Königsberg and ending with the first textbook on the subject, published in 1936 by Dénes Kőnig .
A graph that is locally H is claw-free if and only if the independence number of H is at most two; for instance, the graph of the regular icosahedron is claw-free because it is locally C 5 and C 5 has independence number two. The locally linear graphs are the graphs in which every neighbourhood is an induced matching. [5]
Pearls in Graph Theory: A Comprehensive Introduction is an undergraduate-level textbook on graph theory by Nora Hartsfield and Gerhard Ringel.It was published in 1990 by Academic Press [1] [2] [3] with a revised edition in 1994 [4] and a paperback reprint of the revised edition by Dover Books in 2003. [5]
In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently defined as graphs with clique number ≤ 2, graphs with girth ≥ 4, graphs with no induced 3-cycle , or locally independent graphs.
In the mathematical field of graph theory, the Harries graph or Harries (3-10)-cage is a 3-regular, undirected graph with 70 vertices and 105 edges. [1] The Harries graph has chromatic number 2, chromatic index 3, radius 6, diameter 6, girth 10 and is Hamiltonian. It is also a 3-vertex-connected and 3-edge-connected, non-planar, cubic graph.
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