Geodesic
Maximal outerplane graphs of extremal diameter
Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 4, pp. 421-437

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We explore the maximal outerplane graphs (MOP-graphs) with extremal values of diameter. For arbitrary MOP-graphs we determine the lower and upper bounds of the diameter. For lattice MOP-graphs (i. e., graphs embedded into the lattice of equilateral triangles without "holes" and intersections) we prove that the upper bound of the diameter matches that of the arbitrary MOP-graphs; a preliminary lower bound of the diameter is determined. For the lower and upper bounds of the diameter of arbitrary and lattice MOP-graphs we determine the extremal graphs where these bounds are reached. Extremal graphs with maximal diameter are the same for both arbitrary and lattice MOP-graphs. The obtained results can be used for classification of images represented by MOP-graphs, and for classification of isomers of conjugated polyene hydrocarbons.
Keywords: maximal outerplane graphs, diameter, extremal graphs, graphs with extremal values of diameter. 
@article{CHFMJ_2018_3_4_a3,
     author = {Yu. L. Nosov},
     title = {Maximal outerplane graphs of extremal diameter},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {421--437},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_4_a3/}
}
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Yu. L. Nosov. Maximal outerplane graphs of extremal diameter. Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 4, pp. 421-437. http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_4_a3/