Abstract
Let be a graph. A function is said to be a balanced cycle dominating function (BCDF) of if holds for any induced cycle of The balanced cycle domination number of is defined as A graph is said to be a signed cycle balanced graph (SCB-graph) if there exists a function such that holds for any induced cycle of and is said to be a signed cycle balanced dominating function (SCBDF) of The signed cycle balanced domination number of is defined as In this paper, we present upper bounds for balanced cycle domination number and signed cycle balanced domination number. The exact values of this parameter are determined for a few classes of graphs.
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