The Hermitian-adjacency Spectrum Of Some Operations Of A Mixed Graph

Let G=(V(G).E(G),E(G))be a mixed graph,where V(G)= {v1,v2,…,vv?is the vertex set,E(G)= E(G)U E(G)= ?e1,e2,...,e?} is the edge set,E(G)is the set of undirected edges in G,and E(G)is the set of arcs,or directed edges in G.Let H(G)be the Hermitain-adjacency matrix of G and H-spectrum be the spectrum of H(G).If E(G)=(?)and E(G)?(?),,G is a general simple graph.As we all know,the adjacency spectra of the line graph L(G),subdivision graph S(G),middle graph M(G),R-graph R(G)and total graph T(G)of a k-regular simple graph G can be determined completely by the adjacency spectrum of G.The adjacency spectrum of the line graph L(G)of a semiregular simple graph G can be determined completely by the adjacency spectrum of G.In this paper,we define the line graph L(G),subdivision graph S(G),middle graph M(G),R-graph R(G)and total graph T(G)of a mixed graph G.And,we prove that if G is a k-regular mixed graph,then the H-spectra of L(G),S(G),M(G),R(G)and T(G)can be determined completely by the H-spectrum of G.We also prove that the H-spectrum of the line graph of a semiregular mixed graph G can be expressed completely by the one of G.what's more,all the results are the generalizations of a simple graph.