This paper presents bounds for the variation of the spectral radius λ(G) of a graph G after some perturbations or local vertex/edge modifications of G. The perturbations considered here are the connection of a new vertex with, say, g vertices of G, the addition of a pendant edge (the previous case with g = 1) and the addition of an edge. The method proposed here is based on continuous perturbat...

For any graph H, let Forb∗(H) be the class of graphs with no induced subdivision of H. It was conjectured in [A.D. Scott, Induced trees in graphs of large chromatic number, Journal of Graph Theory, 24:297– 311, 1997] that, for every graph H, there is a function fH : N → R such that for every graph G ∈ Forb∗(H), χ(G) ≤ fH(ω(G)). We prove this conjecture for several graphs H, namely the paw (a tr...

A caterpillar graph is a tree which on removal of all its pendant vertices leaves a chordless path. The chordless path is called the backbone of the graph. The edges from the backbone to the pendant vertices are called the hairs of the caterpillar graph. Ortiz and Villanueva (C.Ortiz and M.Villanueva, Discrete Applied Mathematics, 160(3): 259-266, 2012) describe an algorithm, linear in the size...

The interfacial activity of 3.5 nm homogeneous (HPs) and amphiphilic Janus gold nanoparticles (JPs) was characterized by pendant drop tensiometry for water/air and water/decane interfaces. This technique requires a smaller quantity of nanoparticles than the traditional Langmuir balance technique. The direct deposition at the interface of the nanoparticles dispersed in a spreading solvent also r...

Synthesis, characterization, and properties of new thermally curable polysulfone containing benzoxazine moieties in the side chain were investigated. First, chloromethylation and subsequent azidation processes were performed to form polysulfone containing pendant clickable azide groups. Independently, antagonist 3,4-dihydro-3-(prop-2-ynyl)-2H-benzoxazine was prepared by using paraformaldehyde, ...

a binuclear macrocyclic ligand containing dissimilar n(amine)2o2 and n(imine)2o2 coordination sites sharing two phenolic oxygen atoms, was prepared by cyclic condensation of dialdehyde precursor l1h2 with 1,3-diaminopropane. the ligand includes two propionitrile pendant arms on the amine nitrogen atoms. the homobimetallic complex [znl2zn(oac)]pf6 was synthesized by one step procedure. heterobim...

‎A tree containing exactly two non-pendant vertices is called a double-star‎. ‎Let $k_1$ and $k_2$ be two positive integers‎. ‎The double-star with degree sequence $(k_1+1‎, ‎k_2+1‎, ‎1‎, ‎ldots‎, ‎1)$ is denoted by $S_{k_1‎, ‎k_2}$‎. ‎It is known that a cubic graph has an $S_{1,1}$-decomposition if and only if it contains a perfect matching‎. ‎In this paper‎, ‎we study the $S_{1,2}$-decomposit...

Interactions between electrodes and pendant groups in cross-conjugated systems destroy destructive quantum interference resulting an increase of G a decrease S .