Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXLIII, No. 36, pp. 37–47 (2011) 

One–two descriptor of graphsK. CH. Das, I. Gutman and D. VukicevicDepartment of Mathematics, Sungkyunkwan University, Suwon 440746, Republic of KoreaFaculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia Faculty of Natural Sciences and Mathematics, University of Split, Nikole Tesle 12, 21000 Split, Croatia Abstract: In a recent paper [Vukicevic et al., J. Math. Chem. 48 (2010) 395400] a novel molecular–graph–based structure descriptor, named one–two descriptor ($OT$), was introduced. $OT$ is the sum of vertex contributions, such that each pendent vertex contributes 1, each vertex of degree two adjacent to a pendent vertex contributes 2, and each vertex of degree higher than two also contributes 2. Vertices of degree two, not adjacent to a pendent vertex, do not contribute to $OT$. Vukucevic et al. established lower and upper bounds on $OT$ for trees. We now give lower and upper bounds on $OT$ for general graphs, and also characterize the extremal graphs. The bounds of Vukicevic et al. for trees follows as a special case. Moreover, we give another upper bound on $OT$ for trees. Keywords: one–two descriptor, graph (molecular), degree (of vertex), molecular structure descriptor Classification (MSC2000): 05C07 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 9 Oct 2011. This page was last modified: 8 Apr 2013.
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