Self‐Centered Graphs

On the eccentric distance sum of trees and unicyclic graphs

“…The graphs with rad(G) = diam(G) = d are called self-centered graphs [3] and for such graphs it holds…”

“…For even d we have Similarly, for odd d we have Therefore, we have the following chain of inequalities 3 ) · · · ξ d (C n,n−2 ) ξ d (C n,n−1 ) = ξ d (P n ).…”

Wiener Index of Hexagonal Chains with Segments of Equal Length

“…For example, if we take, as the centrality index, the vertex degree, then heterogeneous networks are precisely antiregular graphs (i.e., graphs with exactly two vertices of the same degree; see [4,30]), while the homogeneous ones are regular graphs. Similarly, the homogeneous graphs with respect to vertex eccentricity are self-centered graphs (see [8]). Here, we will concentrate on graphs whose vertices possess the same value of betweenness centrality; we will call them betweenness-uniform graphs.…”

Cubic Graphs with Application

“…Borzooei and Rashmanlou [7] studied Cayley interval-valued fuzzy threshold graphs. Buckley [8] introduced self-centered graphs. Sunitha et al [25] characterized g-self centered fuzzy graphs.…”