Affiliation: | a Escuela de Ingenieria Comercial, Universidad Adolfo Ibanez, Balmaceda 1625, Vina del Mar, Chile b Department of Mathematics and Statistics, Grand Valley State University, Allendale, MI 49401, USA c Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008, USA |
Abstract: | For a graph G of size m1 and edge-induced subgraphs F and H of size k (1km), the subgraph H is said to be obtained from F by an edge jump if there exist four distinct vertices u,v,w, and x in G such that uvE(F), wxE(G)−E(F), and H=F−uv+wx. The minimum number of edge jumps required to transform F into H is the k-jump distance from F to H. For a graph G of size m1 and an integer k with 1km, the k-jump graph Jk(G) is that graph whose vertices correspond to the edge-induced subgraphs of size k of G and where two vertices of Jk(G) are adjacent if and only if the k-jump distance between the corresponding subgraphs is 1. All connected graphs G for which J2(G) is planar are determined. |