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The harmonic index of unicyclic graphs.

Authors :
Rasi, R.
Sheikholeslami, S. M.
Source :
Asian-European Journal of Mathematics; Sep2017, Vol. 10 Issue 3, p-1, 10p
Publication Year :
2017

Abstract

The harmonic index of a graph , denoted by , is defined as the sum of weights over all edges of , where denotes the degree of a vertex . Hu and Zhou [ WSEAS Trans. Math. 12 (2013) 716-726] proved that for any unicyclic graph of order , with equality if and only if . Recently, Zhong and Cui [ Filomat 29 (2015) 673-686] generalized the above bound and proved that for any unicyclic graph of order other than , . In this paper, we generalize the aforemention results and show that for any connected unicyclic graph of order with maximum degree , and classify the extremal unicyclic graphs. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
17935571
Volume :
10
Issue :
3
Database :
Complementary Index
Journal :
Asian-European Journal of Mathematics
Publication Type :
Academic Journal
Accession number :
125144999
Full Text :
https://doi.org/10.1142/S1793557117500395