Paper Info
Title
Vertex-Degree Based Topological Indices Of Digraphs
Abstract
Let D-n be the set of digraphs with n non-isolated vertices. Let D is an element of D-n and denote by d(u)(+) and d(u)(-) the outer degree and inner degree, respectively, of the vertex u of D. We define the vertex-degree-based (VDB, for short) topological index phi induced by the real numbers {phi(ij)} , asphi(D) = 1/2 Sigma(1 <= i,j <= n-1) a(ij)phi(ij),where a(ij) is the number of arcs in D of the form uv, where d(u)(+) = i and d(v)(-) = j. We show in this paper that this is a generalization of the concept of VDB topological indices of graphs. In the case phi(ij) = 1/root ij, = we obtain the Randic index of digraphs, which we denote by chi. We find the extremal values of chi over D-n. We also find the extremal values of chi over OT((n)), the set of all oriented trees with n vertices. On the other hand, given a graph G, we consider the set O (G) of all orientations of G, and show that when G is a bipartite graph, the sink-source orientations of G uniquely attain the minimal value of chi over O (G). We find the extremal values of chi over O (P-n) and O (C-n), where P-n and C-n are the path and the cycle with n vertices, respectively. Finally, we find the extremal values of chi over O (H-d), the set of all orientations of the hypercube H-d of dimension d. (C) 2021 Elsevier B.V. All rights reserved.
Year
DOI
Venue
2021
10.1016/j.dam.2021.02.024
DISCRETE APPLIED MATHEMATICS
Keywords
DocType
Volume
Degree-based topological index, Randle index, Digraphs, Orientations, Hypercubes, Extremal values
Journal
295
ISSN
Citations 
PageRank 
0166-218X
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Juan Monsalve100.68
Juan Rada201.35