TY - JOUR
ID - 114239
TI - Multiplicative Zagreb Indices and Extremal Complexity of Line Graphs
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Doslic, Tomislav
AD - University of Zagreb Faculty of Civil Engineering, Zagreb, Croatia
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Faculty of Information Studies, Novo Mesto, Slovenia
Y1 - 2024
PY - 2024
VL - 15
IS - 1
SP - 7
EP - 16
KW - Multiplicative Zagreb indices
KW - Complexity
KW - Spanning tree
KW - unicyclic graph
KW - line graph
DO - 10.22052/ijmc.2024.254173.1810
N2 - The number of spanning trees of a graph $G$ is called the complexity of $G$. It is known that the complexity of the line graph of a given graph $G$ can be computed as the sum over all spanning trees of $G$ of contributions which depend on various types of products of degrees of vertices of $G$. We interpret the contributions in terms of three types of multiplicative Zagreb indices, obtaining simple and compact expressions for the complexity of line graphs of graphs with low cyclomatic numbers. As an application, we determine the unicyclic graphs whose line graphs have the smallest and the largest complexity.
UR - https://ijmc.kashanu.ac.ir/article_114239.html
L1 - https://ijmc.kashanu.ac.ir/article_114239_e0925a159e8eb266470e204ab0d5b2ca.pdf
ER -