Compact Valence Sequences for Molecules with Single, Double and Triple Covalent Bonds. Ⅱ. Graphs with Non-trivial Cycles

摘要

Molecular graphs able to model covalent multiple bonds are called plerographs. For such graphs, with single, double and triple edges, compact degree sequences (n_1, n_2, n_3, n_4), where n_i, i = 1, 2, 3, 4 denote the number of vertices of degree i, are defined. Investigations are extended to necessary and sufficient conditions on (n_1, n_2, n_3, n_4) for the existence of graph G such that G has n_1, n_2, n_3 and n_4 vertices of degrees 1, 2, 3 and 4. Namely, graphs with nontrivial cycles with at least three vertices are allowed.%Molekularni grafovi koji mogu modelirati višestruke kovalentne veze zovu se plerografovi. Za takve grafove s jednostrukim, dvostrukim i trostrukim vezama definiran je kompaktni niz stupnjeva (n_1, n_2, n_3, n_4), gdje n_i, i = 1, 2, 3, 4 predstavlja broj vrhova stupnja i. Ovime je nastavljeno istraživanje nužnih i dovoljnih uvjeta na (n_1, n_2, n_3, n_4) za postojanje grafa G, takvog da G ima n_1, n_2, n_3 i n_4 vrhova stupnja 1, 2, 3, 4. Naime, ovdje su dopušteni i grafovi s netrivijalnim ciklusima (ciklusima s barem 3 vrha).