Title of article :
The distance spectrum of two new operations of graphs
Author/Authors :
Tang, Zikai Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) - College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, China , Wu, Renfang Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) - College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, China , Chen, Hanlin Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) - College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, China , Deng, Hanyuan Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) - College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, China
Abstract :
Let G be a connected graph with vertex set V(G)={v1,v2,…,vn}. The distance matrix D=D(G) of G is defined so that its (i,j)-entry is equal to the distance dG(vi,vj) between the vertices vi and vj of G. The eigenvalues μ1,μ2,…,μn of D(G) are the D-eigenvalues of G and form the distance spectrum or the D-spectrum of G, denoted by SpecD(G). In this paper, we introduce two new operations G1■kG2 and G1⧫kG2 on graphs G1 and G2, and describe the distance spectra of G1■kG2 and G1⧫kG2 of regular graphs G1 and G2 in terms of their adjacency spectra. By using these results, we obtain some new integral adjacency spectrum graphs, integral distance spectrum graphs and a number of families of sets of noncospectral graphs with equal distance energy.
Keywords :
Adjacency spectrum , Distance spectrum , Distance energy
Journal title :
Transactions on Combinatorics
