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We discuss solutions of the minimum energy problem in one dimensionalwireless sensor networks for the data transmission cost function $E(x_i,x_j) =d(x_i,x_j)^a + \lambda \;d(x_i,x_j)^b$ with any exponent $a,b\in R$ and$\lambda \geq 0$, where $d(x_i,x_j)$ is a distance between transmitter andreceiver. We define the minimum energy problem in terms of sensors signalpower, transmission time and capacities of a transmission channels. We prove,that for the point-to-point data transmission method utilized by the sensors inthe physical layer, when the transmitter adjust the power of its radio signalto the distance to the receiver, the solutions of the minimum energy problemwritten in terms of data transmission cost function and in terms of the sensorssignal power coincide.

On the solutions of the minimum energy problem in one dimensional sensor networks