Total eccentricity index of graphs with fixed number of pendant or cut vertices

2020/12/02 by Pandey, Dinesh, Patra, Kamal Lochan
#05C05 #05C12 #05C35 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.01090

Abstract

The total eccentricity index of a connected graph is defined as sum of the eccentricities of all its vertices. We denote the set of all connected graphs on n vertices with k pendant vertices by \mathfrakH_n,k and denote the set of all connected graphs on n vertices with s cut vertices by \mathfrakC_n,s. In this paper, we give the sharp lower and upper bounds on the total eccentricity index over \mathfrakH_n,k and the sharp lower bound for the same over \mathfrakC_n,s. We also provide the sharp upper bounds on the total eccentricity index over \mathfrakC_n,s when s=0,1,n-3,n-2 and propose a problem regarding the upper bound over \mathfrakC_n,s for 2≤ s≤ n-4.

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