Title of article :
On Eccentricity Version of Zagreb Coindices
Author/Authors :
Azari, Mahdieh Department of Mathematics - Islamic Azad University Kazerun Branch, Kazerun, Iran
Abstract :
The eccentric connectivity coindex has recently been introduced (Hua and
Miao, 2019) as the total eccentricity sum of all pairs of non-adjacent vertices
in a graph. Considering the total eccentricity product of non-adjacent vertex
pairs, we introduce here another invariant of connected graphs called the
second Zagreb eccentricity coindex. We study some mathematical properties
of the eccentric connectivity coindex and second Zagreb eccentricity coindex.
We also determine the extremal values of the second Zagreb eccentricity
coindex over some specific families of graphs such as trees, unicyclic graphs,
connected graphs, and connected bipartite graphs and describe the extremal
graphs. Moreover, we compare the second Zagreb eccentricity coindex with
the eccentric connectivity coindex and give directions for further studies.
Keywords :
distance in graph , vertex eccentricity , bound , extremal graphs
Journal title :
Control and Optimization in Applied Mathematics