Euclidean graph distance matrices of generalizations of the star graph

2014 ◽  
Vol 230 ◽  
pp. 650-663 ◽  
Author(s):  
Gašper Jaklič ◽  
Jolanda Modic
Keyword(s):  
Star Graph ◽  
Graph Distance ◽  
Distance Matrices

FUZZY MAGIC LABELLING OF NEUTROSOPHIC PATH AND STAR GRAPH

2020 ◽  
Vol 9 (8) ◽  
pp. 6059-6070
Author(s):  
D. Ajay ◽  
P. Chellamani
Keyword(s):  
Star Graph

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

Fault tolerance of the star graph interconnection network

1994 ◽  
Vol 49 (3) ◽  
pp. 145-150 ◽  
Author(s):  
Zoran Jovanović ◽  
Jelena Mišić
Keyword(s):  
Fault Tolerance ◽  
Interconnection Network ◽  
Star Graph
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