Geodesic
Husimi trees
Matematičeskie zametki, Tome 9 (1971) no. 3, pp. 253-262.

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The problem is solved of the construction of a Husimi tree (a connected graph in which each line belongs to not more than one simple cycle) for the case in which the length of simple cycles and the distance between any two points of $x_1, x_2, \dots, x_n$ is known, where $\{x_1, x_2, \dots, x_n\}$ is the set of all simple cycles and all hanging points. A necessary and sufficient condition is found for the existence of such a Husimi tree and its uniqueness is proved. 
@article{MZM_1971_9_3_a3,
     author = {K. A. Zaretskii},
     title = {Husimi trees},
     journal = {Matemati\v{c}eskie zametki},
     pages = {253--262},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_3_a3/}
}
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K. A. Zaretskii. Husimi trees. Matematičeskie zametki, Tome 9 (1971) no. 3, pp. 253-262. http://geodesic.mathdoc.fr/item/MZM_1971_9_3_a3/