Geodesic
Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 75 (2014) no. 2, pp. 125-138

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We study the inverse problem of recovering differential operators from spectra on compact star-type graphs when differential equations have different orders on different edges. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness. 
@article{MMO_2014_75_2_a2,
     author = {V. A. Yurko},
     title = {Inverse {Problem} for {Differential} {Operators} on {Spatial} {Networks} with {Different} {Orders} on {Different} {Edges}},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {125--138},
     publisher = {mathdoc},
     volume = {75},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a2/}
}
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V. A. Yurko. Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 75 (2014) no. 2, pp. 125-138. http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a2/