Geodesic
Scaling Graphs with Diameter Constraint
Diskretnaya Matematika, Tome 35 (2023) no. 4, pp. 46-57

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The influence of the gluing and cloning on operations of subgraphs on the graph diameter is studied. The vertex-diameter graphs are defined as graphs, all vertices of which belong to diametric chains. The possibilities of their use in scaling graphs with a diameter limitation are considered. Examples of scaling of trees, fat trees, and vertex-diameter graphs using the operations of cloning and gluing are given. The diameter and complexity of the synthesis of such graphs are estimated.
Keywords: trees, fat trees, vertex-diameter graphs, diameter, dominating set with neighborhood, gluing and cloning operations. 
@article{DM_2023_35_4_a2,
     author = {M. A. Iordanskii},
     title = {Scaling {Graphs} with {Diameter} {Constraint}},
     journal = {Diskretnaya Matematika},
     pages = {46--57},
     publisher = {mathdoc},
     volume = {35},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2023_35_4_a2/}
}
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M. A. Iordanskii. Scaling Graphs with Diameter Constraint. Diskretnaya Matematika, Tome 35 (2023) no. 4, pp. 46-57. http://geodesic.mathdoc.fr/item/DM_2023_35_4_a2/