TY - JOUR
ID - 110827
TI - On the Modified First Zagreb Connection Index of Trees of a Fixed Order and Number of Branching Vertices
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Noureen, Sadia
AU - Bhatti, Akhlaq Ahmad
AU - Ali, Akbar
AD - National University of Computer and Emerging Sciences, Lahore, Pakistan
AD - National University of Computer and
Emerging Sciences, Lahore, Pakistan
AD - University of Hail, Hail, Saudi Arabia
Y1 - 2020
PY - 2020
VL - 11
IS - 4
SP - 213
EP - 226
KW - Chemical graph theory
KW - topological index
KW - Zagreb connection indices
KW - extremal problem
DO - 10.22052/ijmc.2020.240260.1514
N2 - The modified first Zagreb connection index $ZC_{1}^{*}$ for a graph $G$ is defined as $ZC_{1}^{*}(G)= \sum_{v\in V(G)}d_{v}\tau_{v}\,$, where $d_{v}$ is degree of the vertex $v$ and $\tau _{v}$ is the connection number of $v$ (that is, the number of vertices having distance 2 from $v$). By an $n$-vertex graph, we mean a graph of order $n$. A branching vertex of a graph is a vertex with degree greater than $2$. In this paper, the graphs with maximum and minimum $ZC_{1}^{*}$ values are characterized from the class of all $n$-vertex trees with a fixed number of branching vertices.
UR - https://ijmc.kashanu.ac.ir/article_110827.html
L1 - https://ijmc.kashanu.ac.ir/article_110827_9963a63de0e8366746c57fc8870654ad.pdf
ER -