The fundamental theorem on linear programming

1961 ◽  
Vol 54 (1) ◽  
pp. 25-26
Author(s):  
Shmuel Avital
Keyword(s):  
Linear Programming ◽  
Fundamental Theorem ◽  
Convex Polygon ◽  
Minimum Value

An expression ax+by defined over a closed convex polygon assumes its maximum and minimum value at one (or more) of the vertices of the polygon.

scholarly journals An extension of the fundamental theorem of linear programming

2002 ◽  
Vol 30 (5) ◽  
pp. 281-288 ◽  
Author(s):  
A. Brown ◽  
A. Gedlaman ◽  
A. Holder ◽  
S. Martinez
Keyword(s):  
Linear Programming ◽  
Fundamental Theorem

The minimum value of the harmonic index for a graph with the minimum degree two

2018 ◽  
Vol 13 (03) ◽  
pp. 2050054 ◽  
Author(s):  
Hanyuan Deng ◽  
S. Balachandran ◽  
S. Raja Balachandar
Keyword(s):  
Linear Programming ◽  
Connected Graph ◽  
Minimum Degree ◽  
Harmonic Index ◽  
Minimum Value ◽  
Degree Of A Vertex

For a simple and connected graph [Formula: see text] with [Formula: see text] vertices and the minimum degree two, we show that [Formula: see text] by a technique based on linear programming, where [Formula: see text] is the harmonic index of a graph [Formula: see text], defined as the sum of the weights [Formula: see text] of all edges [Formula: see text] of [Formula: see text], [Formula: see text] denotes the degree of a vertex [Formula: see text], and characterize the graph with the minimum value.

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