Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4648933 | Discrete Mathematics | 2007 | 7 Pages |
Abstract
For a graph G , the middle graph M(G)M(G) of G is the graph with vertex set V(G)∪E(G)V(G)∪E(G) in which the vertices x and y are joined by an edge if {x,y}∩E(G)≠∅{x,y}∩E(G)≠∅, and x and y are adjacent or incident in G . In this note, we show that the complement of middle graph M(G)M(G) of a graph G is hamiltonian if and only if G is not a star and is not isomorphic to any graph in {K1,2K1,K2,K2∪K1,K3,K3∪K1}{K1,2K1,K2,K2∪K1,K3,K3∪K1}.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Xinhui An, Baoyindureng Wu,