TY - JOUR
T1 - On the Zagreb and Eccentricity Coindices of Graph Products
TT -
JF - IJMSI
JO - IJMSI
VL - 18
IS - 1
UR - http://ijmsi.ir/article-1-1529-en.html
Y1 - 2023
SP - 165
EP - 178
KW - Eccentricity of a vertex
KW - Graph invariants
KW - Graph products
KW - Chemical graphs.
N2 - The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity coindex of some graph products such as lexicographic product, generalized hierarchical product, and strong product. Results are applied to compute the values of this eccentricity-based invariant for some chemical graphs and nanostructures such as hexagonal chain, linear phenylene chain, and zig-zag polyhex nanotube.
M3 10.52547/ijmsi.18.1.165
ER -