2017/11/19 by Farooq, Rashid, Malik, Mehar Ali, Rada, Juan
#5C12 #5C35 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1711.07021
In a connected graph G, the distance between two vertices of G is the length of a shortest path between these vertices. The eccentricity of a vertex u in G is the largest distance between u and any other vertex of G. The total-eccentricity index τ(G) is the sum of eccentricities of all vertices of G. In this paper, we find extremal trees, unicyclic and bicyclic graphs with respect to total-eccentricity index. Moreover, we find extremal conjugated trees with respect to total-eccentricity index.