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

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One–two descriptor of graphs

K. CH. Das, I. Gutman and D. Vukicevic

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
Faculty 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) 395-400] 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

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Electronic fulltext finalized on: 9 Oct 2011. This page was last modified: 8 Apr 2013.

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