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
Keywords: one-two descriptor, graph (molecular), degree (of vertex), molecular structure descriptor
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/
@article{BASS_2011_36_a2,
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 },
year = {2011},
volume = {36},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BASS_2011_36_a2/}
}
TY - JOUR AU - K. CH. Das AU - I. Gutman AU - D. Vukičević TI - One-two descriptor of graphs JO - Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles PY - 2011 SP - 37 VL - 36 UR - http://geodesic.mathdoc.fr/item/BASS_2011_36_a2/ LA - en ID - BASS_2011_36_a2 ER -