TY - JOUR
T1 - Bounds for the eccentricity spectral radius of join digraphs with a fixed dichromatic number
AU - Yang, Xiuwen
AU - Broersma, Hajo
AU - Wang, Ligong
N1 - Publisher Copyright:
© 2024 The Author(s)
PY - 2024/11/15
Y1 - 2024/11/15
N2 - The eccentricity matrix ɛ(G) of a strongly connected digraph G is defined as ɛ(G)ij=d(vi,vj),ifd(vi,vj)=min{e+(vi),e−(vj)},0,otherwise.,where e+(vi)=max{d(vi,vj)∣vj∈V(G)} is the out-eccentricity of the vertex vi of G, and e−(vj)=max{d(vi,vj)∣vi∈V(G)} is the in-eccentricity of the vertex vj of G. The eigenvalue of ɛ(G) with the largest modulus is called the eccentricity spectral radius of G. In this paper, we obtain lower bounds for the eccentricity spectral radius among all join digraphs with a fixed dichromatic number. We also give upper bounds for the eccentricity spectral radius of some special join digraphs with a fixed dichromatic number.
AB - The eccentricity matrix ɛ(G) of a strongly connected digraph G is defined as ɛ(G)ij=d(vi,vj),ifd(vi,vj)=min{e+(vi),e−(vj)},0,otherwise.,where e+(vi)=max{d(vi,vj)∣vj∈V(G)} is the out-eccentricity of the vertex vi of G, and e−(vj)=max{d(vi,vj)∣vi∈V(G)} is the in-eccentricity of the vertex vj of G. The eigenvalue of ɛ(G) with the largest modulus is called the eccentricity spectral radius of G. In this paper, we obtain lower bounds for the eccentricity spectral radius among all join digraphs with a fixed dichromatic number. We also give upper bounds for the eccentricity spectral radius of some special join digraphs with a fixed dichromatic number.
KW - UT-Hybrid-D
KW - Eccentricity matrix
KW - Spectral radius
KW - Dichromatic number
UR - http://www.scopus.com/inward/record.url?scp=85196630183&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2024.06.019
DO - 10.1016/j.dam.2024.06.019
M3 - Article
AN - SCOPUS:85196630183
SN - 0166-218X
VL - 357
SP - 241
EP - 257
JO - Discrete applied mathematics
JF - Discrete applied mathematics
ER -