TY - JOUR
T1 - Hermitian-Randić matrix and Hermitian-Randić energy of mixed graphs
AU - Lu, Yong
AU - Wang, Ligong
AU - Zhou, Qiannan
N1 - Publisher Copyright:
© 2017, The Author(s).
PY - 2017/12/1
Y1 - 2017/12/1
N2 - Let M be a mixed graph and H(M) be its Hermitian-adjacency matrix. If we add a Randić weight to every edge and arc in M, then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix? Motivated by this, we define the Hermitian-Randić matrix RH(M)=(rh)kl of a mixed graph M, where (rh)kl=−(rh)lk=idkdl (i=−1) if (vk, vl) is an arc of M, (rh)kl=(rh)lk=1dkdl if vkvl is an undirected edge of M, and (rh)kl=0 otherwise. In this paper, firstly, we compute the characteristic polynomial of the Hermitian-Randić matrix of a mixed graph. Furthermore, we give bounds on the Hermitian-Randić energy of a general mixed graph. Finally, we give some results about the Hermitian-Randić energy of mixed trees.
AB - Let M be a mixed graph and H(M) be its Hermitian-adjacency matrix. If we add a Randić weight to every edge and arc in M, then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix? Motivated by this, we define the Hermitian-Randić matrix RH(M)=(rh)kl of a mixed graph M, where (rh)kl=−(rh)lk=idkdl (i=−1) if (vk, vl) is an arc of M, (rh)kl=(rh)lk=1dkdl if vkvl is an undirected edge of M, and (rh)kl=0 otherwise. In this paper, firstly, we compute the characteristic polynomial of the Hermitian-Randić matrix of a mixed graph. Furthermore, we give bounds on the Hermitian-Randić energy of a general mixed graph. Finally, we give some results about the Hermitian-Randić energy of mixed trees.
KW - Hermitian-adjacency matrix
KW - Hermitian-Randić energy
KW - Hermitian-Randić matrix
KW - mixed graph
UR - http://www.scopus.com/inward/record.url?scp=85014535007&partnerID=8YFLogxK
U2 - 10.1186/s13660-017-1329-8
DO - 10.1186/s13660-017-1329-8
M3 - 文章
AN - SCOPUS:85014535007
SN - 1025-5834
VL - 2017
JO - Journal of Inequalities and Applications
JF - Journal of Inequalities and Applications
IS - 1
M1 - 54
ER -