extremal energy
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Author(s):  
N.E. Arévalo ◽  
R.O. Braga ◽  
V.M. Rodrigues
Keyword(s):  


Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4297-4309
Author(s):  
Xiuwen Yang ◽  
Ligong Wang

Let Sn be the class of bicyclic signed digraphs with n vertices whose two signed directed even cycles are vertex-disjoint. In this paper, we characterize the ordering of bicyclic signed digraphs in Sn by energy with two positive or negative directed even cycles (resp., one positive directed even cycle and one negative directed even cycle). Furthermore, we determine extremal energy in Sn by the two orderings.



2019 ◽  
Vol 12 (05) ◽  
pp. 1950078
Author(s):  
Rashid Farooq ◽  
Sarah Chand ◽  
Mehtab Khan

Iota energy of signed digraphs is defined as sum of absolute values of imaginary parts of its eigenvalues. Extremal energy and iota energy of unicyclic signed digraphs is known. In this paper, we address the problem of finding signed digraphs with extremal iota energy among vertex-disjoint bicyclic signed digraphs of fixed order.



2019 ◽  
Vol 13 (05) ◽  
pp. 2050090
Author(s):  
Sumaira Hafeez ◽  
Mehtab Khan

The energy of a weighted digraph [Formula: see text] is the sum of absolute values of real part of its eigenvalues. Recently, the minimal and maximal energy of unicyclic weighted digraphs with cycle weight [Formula: see text] is studied. In this paper, we introduce a class [Formula: see text] of those bicyclic weighted digraphs of fixed order which contain vertex-disjoint weighted cycles of weights [Formula: see text] or [Formula: see text] and [Formula: see text] or [Formula: see text], where [Formula: see text]. We find digraphs in [Formula: see text] under certain conditions on [Formula: see text] and [Formula: see text] with extremal energy.



2016 ◽  
Vol 40 (1) ◽  
pp. 79-89 ◽  
Author(s):  
Rashid Farooq ◽  
Mehtab Khan ◽  
Yasir Masood
Keyword(s):  


2015 ◽  
pp. 799-810 ◽  
Author(s):  
Mehtab Khan ◽  
Rashid Farooq ◽  
Azad A. Siddiqui
Keyword(s):  


2012 ◽  
Vol 60 (11-12) ◽  
pp. 1255-1264
Author(s):  
Richard A. Brualdi ◽  
Jia-Yu Shao ◽  
Shi-Cai Gong ◽  
Chang-Qing Xu ◽  
Guang-Hui Xu


2010 ◽  
Vol 725 (2) ◽  
pp. 1507-1515 ◽  
Author(s):  
Vladimír Karas ◽  
Vjačeslav Sochora


2009 ◽  
Vol 106 (5) ◽  
pp. 753-756 ◽  
Author(s):  
N. V. Grishina ◽  
Yu. A. Eremin ◽  
A. G. Sveshnikov


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