Title of article :
On Middle Cube Graphs
Author/Authors :
Dalfo, Cristina Universitat Politecnica de Catalunya - Departament de Matematica Aplicada IV, Spain , Fiol, Miquel Angel Universitat Politecnica de Catalunya - Departament de Matematica Aplicada IV, Spain , Mitjana, Margarida Universitat Politecnica de Catalunya - Departament de Matematica Aplicada I, Spain
Abstract :
We study a family of graphs related to the n-cube. The middle cube graph of parameter k is thesubgraph of Q2k-1 induced by the set of vertices whose binary representation has either k-1 ork number of ones. The middle cube graphs can be obtained from the well-known odd graphs bydoubling their vertex set. Here we study some of the properties of the middle cube graphs in thelight of the theory of distance-regular graphs. In particular, we completely determine their spectra(eigenvalues and their multiplicities, and associated eigenvectors).
Keywords :
distance , regular graph , odd graph , spectrum
Journal title :
Electronic Journal of Graph Theory and Applications (EJGTA)
Journal title :
Electronic Journal of Graph Theory and Applications (EJGTA)
