Year: 2024
Type: article
Abstract: Let G be a simple connected graph with vertices v1, v2 . . ., vn.The distance matrix of G, denoted by D(G), is the n × n matrix whose (i, j) th element is equal to d(vi, vj) (the length of a shortest path between vi and vj).Let P(n, r) be the family of all connected graphs of order n having r pendant vertices.In this paper, we obtain the distance spectrum of various subfamilies of P(n, r), like pineapple graphs, kite graphs, double star graphs, etc.We also determine the graphs with the largest and smallest spectral radii belonging to these families.Finally, we give a lower bound for the smallest distance eigenvalue of certain kite graphs in terms of minimum transmission.
Source: Discrete Mathematics Letters
Authors: Shariefuddin Pirzada, Ummer Mushtaq, Yilun Shang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Award: G8840562462
OpenAlex ID: W4403341224