Geodesic
One-two descriptor of graphs
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 36 (2011), p. 37 .

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In a recent paper [Vukičević et al., J. Math. Chem. {\bf 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 $OT$. Vukučević 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 Vukičević et al. for trees follows as a special case. Moreover, we give another upper bound on $OT$ for trees.
Classification : 05C07
Keywords: one-two descriptor, graph (molecular), degree (of vertex), molecular structure descriptor 
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     author = {K. CH. Das and I. Gutman and D. Vuki\v{c}evi\'c},
     title = {One-two descriptor of graphs},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {37 },
     publisher = {mathdoc},
     volume = {36},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2011_36_a2/}
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K. CH. Das; I. Gutman; D. Vukičević. One-two descriptor of graphs. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 36 (2011), p. 37 . http://geodesic.mathdoc.fr/item/BASS_2011_36_a2/