TY - JOUR
T1 - The α-index of graphs without intersecting triangles/quadrangles as a minor
AU - Zhang, Yanting
AU - Wang, Ligong
N1 - Publisher Copyright:
© 2024 Elsevier B.V.
PY - 2025/1/30
Y1 - 2025/1/30
N2 - The Aα-matrix of a graph G is the convex linear combination of the adjacency matrix A(G) and the diagonal matrix of vertex degrees D(G), i.e., Aα(G)=αD(G)+(1−α)A(G), where 0≤α≤1. The α-index of G is the largest eigenvalue of Aα(G). In this paper, we characterize the extremal graphs with the maximum α-index among all graphs of sufficiently large order without intersecting triangles and quadrangles as a minor for any 0<α<1, respectively. As by-products, we determine the extremal graphs with the maximum signless Laplacian spectral radius over all graphs of sufficiently large order without intersecting triangles and quadrangles as a minor, respectively.
AB - The Aα-matrix of a graph G is the convex linear combination of the adjacency matrix A(G) and the diagonal matrix of vertex degrees D(G), i.e., Aα(G)=αD(G)+(1−α)A(G), where 0≤α≤1. The α-index of G is the largest eigenvalue of Aα(G). In this paper, we characterize the extremal graphs with the maximum α-index among all graphs of sufficiently large order without intersecting triangles and quadrangles as a minor for any 0<α<1, respectively. As by-products, we determine the extremal graphs with the maximum signless Laplacian spectral radius over all graphs of sufficiently large order without intersecting triangles and quadrangles as a minor, respectively.
KW - Extremal graph
KW - Intersecting quadrangles
KW - Intersecting triangles
KW - Minor
KW - α-index
UR - http://www.scopus.com/inward/record.url?scp=85208669074&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2024.10.027
DO - 10.1016/j.dam.2024.10.027
M3 - 文章
AN - SCOPUS:85208669074
SN - 0166-218X
VL - 361
SP - 324
EP - 335
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -