The Randić index of a graph G, denoted by R(G), is defined as the sum 1/d(u)d(v) for all edges uv where d(u) denotes degree vertex u in G. In this note, we show that R(L(T))>n4 any tree T order n≥3. A number relevant conjectures are proposed.

the dispersibility of graphene is modeled as a mathematical function of the molecular structure of solvent represented by simplified molecular input-line entry systems (smiles) together with the graph of atomic orbitals (gao). the gao is molecular graph where atomic orbitals e.g. 1s1, 2p4, 3d7 etc., are vertexes of the graph instead of the chemical elements used as the graph vertexes in the tra...

We observe that ω(G) + χ(S( G)) = n = ω(S( G)) + χ(G) for any graph G with n vertices, where G is any acyclic orientation of G and where S( G) is the (complement of the) auxiliary line graph introduced in [1]. (Where as usual, ω and χ denote the clique number and the chromatic number.) It follows that, for any graph parameter β(G) sandwiched between ω(G) and χ(G), then Φβ( G) := n−β(S( G)) is s...

abstract background: a major problem of the first moments of childbirth, especially in “prolonged labor,” is perinatal asphyxia which necessitates neonatal resuscitation. this study aimed at evaluating the alert line of the partogram in recognizing the need for neonatal resuscitation 20–30 s after delivery. materials and methods: 140 full‑term pregnant women were kept under surveillance through...