Graph equation
Open-knowledge reference entry
In graph theory, Graph equations are equations in which the unknowns are graphs. One of the central questions of graph theory concerns the notion of isomorphism. We ask: When are two graphs the same? (i.e., graph isomorphism) The graphs in question may be expressed differently in terms of graph equations.
What are the graphs (solutions) G and H such that the line graph of G is same as the total graph of H? (What are G and H such that L(G) = T(H) ?).
For example, G = K3, and H = K2 are the solutions of the graph equation L(K3) = T(K2) and G = K4, and H = K3 are the solutions of the graph equation L(K4) = T(K3).
Note that T(K3) is a 4-regular graph on 6 vertices.
Selected publications
Graph equations for line graphs and total graphs, DM Cvetkovic, SK Simic – Discrete Mathematics, 1975
Graph equations, graph inequalities and a fixed point theorem, DM Cvetkovic, IB Lackovic, SK Simic – Publ. Inst.
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This entry incorporates text from “Graph equation” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.