Graph Theory

Diestel, R. (2017). Graph Theory. Springer.

Type

Book

Intellectual base

Review or monograph

Year

2017

DOI

10.1007/978-3-662-53622-3

ISBN

9783662536216

Link

https://doi.org/10.1007/978-3-662-53622-3

Cited from

mathematics

Cited by

8 citations across 8 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Cycle
  • The cycle supports several reusable inference patterns, each stated in terms of closed paths rather than any substrate. Cycle space: the cycles of a graph form a vector space over the two-element field whose dimension is edges minus vertices plus components, giving a structural counting principle and a basis for cycle decomposition.

    This sourceEstablishes the cycle space of a graph as a vector space over GF(2) of dimension (edges − vertices + components), giving the cycle-counting principle and a basis for cycle decomposition.

Domain-specific

• Clique (Graph Theory)
  • Equivalently, the subgraph induced by \(C\) is complete.
• Clique-sum
  • A clique-sum is a graph-composition operation that takes the disjoint union of two graphs and identifies corresponding vertices of selected equal-order cliques, with interface-edge deletion governed by the chosen convention.
• Dense Graph
  • For a graph sequence, the clean asymptotic regime is \(|E|=\Theta(n^2)\), equivalently density bounded away from zero along the sequence.
• Girth (Graph Theory)
  • Large girth means neighborhoods remain tree-like to a larger radius even when the graph eventually contains cycles.
• Hadwiger number
  • Hadwiger number is the largest integer k such that the complete graph on k vertices occurs as a minor of a given undirected graph.
• Quotient Graph
  • Diestel's treatment of contractions and minors supplies the standard connected-block special case.
• Tree (Set Theory)
  • An ordinary graph edge cannot encode that limit connection without adding different structure.

    This sourceAuthoritative source for the connected-acyclic graph-tree identity used to mark the graph-theoretic boundary.

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