A conservative labeling of a finite undirected graph with 
edges consists of an orientation
and a bijective labeling of the edges
by the integers 1, 2, ..., 
such that, at every vertex,
the sum of labels on incoming edges equals the sum
on outgoing edges (Bange et al. 1980; Gardner
2023, p. 1). A graph admitting a conservative labeling
is a conservative graph.
Conservative Labeling
See also
Conservative Graph, Graph OrientationExplore with Wolfram|Alpha
References
Bange, D. W.; Barkauskas, A. E.; and Slater, P. J. "Conservative Graphs." J. Graph Th. 4, 81-91, 1980. https://doi.org/10.1002/jgt.3190040109.Gardner, R. "Section 6.2. Conservative Graphs." Introduction to Graph Theory--Class Notes. Rev. Jan. 15, 2023. https://faculty.etsu.edu/gardnerr/5347/Notes/Pearls-GT-6-2.pdf.Cite this as:
Weisstein, Eric W. "Conservative Labeling." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ConservativeLabeling.html