TY - JOUR
ID - 110780
TI - On Edge Mostar Index of Graphs
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Liu, Hechao
AU - Song, Ling
AU - Xiao, Qiqi
AU - Tang, Zikai
AD - College of Mathematics and Statistics
Hunan Normal University
AD - School of Mathematics and Statistics, Hunan Normal University
Y1 - 2020
PY - 2020
VL - 11
IS - 2
SP - 95
EP - 106
KW - Edge Mostar index
KW - tree
KW - unicyclic graph
KW - Cacti
KW - Extremal value
DO - 10.22052/ijmc.2020.221320.1489
N2 - The edge Mostar index 𝑀𝑜𝑒(𝐺) of a connected graph 𝐺 is defined as 𝑀𝑜𝑒(𝐺)=Σ𝑒=𝑢𝑣∈𝐸(𝐺) |𝑚𝑢(𝑒|𝐺)−𝑚𝑣(𝑒|𝐺)|, where 𝑚𝑢(𝑒|𝐺)and 𝑚𝑣(𝑒|𝐺) are, respectively, the number of edges of 𝐺 lying closer to vertex 𝑢 than to vertex 𝑣 and the number of edges of 𝐺 lying closer to vertex 𝑣 than to vertex 𝑢. In this paper, we determine the extremal values of edge Mostar index of some graphs. We characterize extremal trees, unicyclic graphs and determine the extremal graphs with maximum and second maximum edge Mostar index among cacti with size 𝑚 and 𝑡 cycles. At last, we give some open problems.
UR - https://ijmc.kashanu.ac.ir/article_110780.html
L1 - https://ijmc.kashanu.ac.ir/article_110780_6c7ca696f01b7ecfc6543d510880bef9.pdf
ER -