Advances and Applications in Discrete Mathematics
Volume 22, Issue 1, Pages 75 - 101
(September 2019) http://dx.doi.org/10.17654/ |
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ALGEBRAIC STRUCTURES RELATED TO BALANCED FUNCTIONS ON GRAPHS: RESULTS AND OPEN PROBLEMS
Yonah Cherniavsky
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Abstract: A group-valued function on a graph is called balanced if the product of its values along any cycle is equal to the identity element of the group. Such functions themselves form a group. In this expository article we discuss our rather recent works on this subject and suggest problems for further investigation. |
Keywords and phrases: consistent graphs, balanced signed graphs, balanced labelings of graphs, gain graphs, weighted graphs, cycle-vanishing valuations.
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