Edge Version of Harmonic Index and Harmonic Polynomial of Rooted Product Graphs

2018 ◽  
Vol 14 ◽  
pp. 239-245 ◽  
Author(s):  
Muhammad Shoaib Sardar ◽  
Rabia Nazir ◽  
Sohail Zafar ◽  
Zohaib Zahid ◽  
Keyword(s):  
Harmonic Polynomial ◽  
Harmonic Index ◽  
Product Graphs

scholarly journals EDGE VERSION OF HARMONIC INDEX AND HARMONIC POLYNOMIAL OF SOME CLASSES OF GRAPHS

2016 ◽  
Vol 34 (5_6) ◽  
pp. 479-486 ◽  
Author(s):  
RABIA NAZIR ◽  
SHOAIB SARDAR ◽  
SOHAIL ZAFAR ◽  
ZOHAIB ZAHID
Keyword(s):  
Harmonic Polynomial ◽  
Harmonic Index

scholarly journals Harmonic Index and Harmonic Polynomial on Graph Operations

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 456 ◽  
Author(s):  
Juan Hernández-Gómez ◽  
J. Méndez-Bermúdez ◽  
José Rodríguez ◽  
José M.  Sigarreta
Keyword(s):  
Lower Bounds ◽  
Convex Functions ◽  
Topological Index ◽  
Cartesian Product ◽  
Harmonic Polynomial ◽  
Upper And Lower Bounds ◽  
Lexicographic Product ◽  
Harmonic Index ◽  
Graph Operations ◽  
Corona Product

Some years ago, the harmonic polynomial was introduced to study the harmonic topological index. Here, using this polynomial, we obtain several properties of the harmonic index of many classical symmetric operations of graphs: Cartesian product, corona product, join, Cartesian sum and lexicographic product. Some upper and lower bounds for the harmonic indices of these operations of graphs, in terms of related indices, are derived from known bounds on the integral of a product on nonnegative convex functions. Besides, we provide an algorithm that computes the harmonic polynomial with complexity O ( n 2 ) .

scholarly journals The harmonic index of product graphs

2017 ◽  
Vol 11 (3) ◽  
pp. 203-209 ◽  
Author(s):  
B. N. Onagh
Keyword(s):  
Harmonic Index ◽  
Product Graphs

rr-SEQUENCE PRODUCT GRAPHS

2020 ◽  
Vol 9 (3) ◽  
pp. 927-936
Author(s):  
S. Avadayappan ◽  
M. Bhuvaneshwari ◽  
S. Vimalajenifer
Keyword(s):  
Product Graphs
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