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1 Examples and types of graphs. ... This is a list of graph theory topics, ... Regular graph; Scale-free network; Snark (graph theory)
The first Harris graph discovered was the Shaw graph, which has order 9 and size 14. [1] [2] [3] This graph served as the counterexample to Harris Spungen's 2013 conjecture. The minimal barnacle-free Harris graph, or the Lopez graph, has order 13 and size 33. It was constructed to address a conjecture that barnacle-free Harris graphs do not ...
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.
The "pearls" of the title include theorems, proofs, problems, and examples in graph theory.The book has ten chapters; after an introductory chapter on basic definitions, the remaining chapters material on graph coloring; Hamiltonian cycles and Euler tours; extremal graph theory; subgraph counting problems including connections to permutations, derangements, and Cayley's formula; graph ...
The Petersen graph is the smallest snark. The flower snark J 5 is one of six snarks on 20 vertices.. In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three colors.
In graph theory, a cograph, or complement-reducible graph, or P 4-free graph, is a graph that can be generated from the single-vertex graph K 1 by complementation and disjoint union. That is, the family of cographs is the smallest class of graphs that includes K 1 and is closed under complementation and disjoint union.
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For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
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