Graph equation
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? The graphs in question may be expressed differently in terms of graph equations.
What are the graphs G and H such that the line graph of G is same as the total graph of H? = T.
For example, G = K3, and H = K2 are the solutions of the graph equation L = T and G = K4, and H = K3 are the solutions of the graph equation L = T.
Note that T 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. Math.., 1976 - elib.mi.sanu.ac.yu, PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE Nouvelle série, tome 20, 1976,
- Graphs whose complement and line graph are isomorphic, M Aigner - Journal of Combinatorial Theory, 1969
- Solutions of some further graph equations, Vasanti N. Bhat-Nayak, Ranjan N. Naik - Discrete Mathematics, 47 169-175
- More Results on the Graph Equation G2= G, M Capobianco, SR Kim - Graph Theory, Combinatorics, and Algorithms: Proceedings of …, 1995 - Wiley-Interscience
- Graph equation Ln = G, S Simic - Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz, 1975