On the computation of extremal trees of Harmonic index with given edge-vertex domination number-Reference-Cited by-同舟云学术

On the computation of extremal trees of Harmonic index with given edge-vertex domination number

Published:2023-03-30 Issue:05 Volume:21 Page:
ISSN:0219-6913
Container-title:International Journal of Wavelets, Multiresolution and Information Processing
language:en
Short-container-title:Int. J. Wavelets Multiresolut Inf. Process.

Author:

Senthilkumar B.¹^ORCID,Kumar H. Naresh¹,Venkatakrishnan Y. B.¹,Raja S. P.²

Affiliation:

1. School of Arts Sciences Humanities and Education, SASTRA Deemed to be University, Thanjavur 613 401, India

2. School of Computer Science and Engineering, Vellore Institute of Technology, Vellore 632 014, Tamilnadu, India

Abstract

Let [Formula: see text] be vertices of a graph [Formula: see text] with degree of the vertices being [Formula: see text] and [Formula: see text] respectively. First, let us define the weight of the edge [Formula: see text] as twice the value of [Formula: see text] in [Formula: see text]. Let us define [Formula: see text], the harmonic index of the graph [Formula: see text], as the sum obtained by adding the weight assigned to every edge of [Formula: see text]. In this paper, for the class of trees, we shall obtain an upper bound for the harmonic index [Formula: see text] in terms of the edge-vertex domination number and the order of [Formula: see text]. Also, we shall ascertain that the equality is true by characterizing the collection of all extremal trees attaining this bound.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Information Systems,Signal Processing

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219691323500145

Reference23 articles.

1. A Multiresolution Approach to the Electric Field Integral Equation in Antenna Problems

2. Graph products and eccentric harmonic index

3. Extremal trees for the Randić index with given domination number

4. On the Weierstrass-Mandelbrot fractal function