Extremal And
نویسنده
چکیده
|We continue the analysis of (r; q)-polycycles, i.e., planar graphs G that admit a realization on the plane such that all internal vertices have degree q, all boundary vertices have degree at most q, and all internal faces are combinatorial r-triangles; moreover, the vertices, edges, and internal faces form a cell complex. Two extremal problems related to chemistry are solved: the description of (r; q)-polycycles with the maximal number of internal vertices for a given number of faces, and the description of nonextendible (r; q)-polycycles. Numerous examples of isohedral polycycles (whose symmetry groups are transitive on faces) are presented.
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