The harmonic index H(G) of a graph G is the sum of 2 d(u) + d(Ï…) over all edges uÏ… of G, where d(u) denotes the degree of a vertex u in G. In this paper, we give the minimum value of H(G) for graphsâ€¦ (More)

The harmonic index H(G) of a graph G is defined as the sum of weights 2 d(u)+d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we have determined the minimumâ€¦ (More)

We say that a simple graph G is fractional independent-set-deletable k-factor-critical, shortly, fractional ID-k-factor-critical, if Gâˆ’I has a fractional k-factor for every independent set I of G.â€¦ (More)

The harmonic index H(G) of a graph G is defined as the sum of weights 2 d(u)+d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we first present a sharp lowerâ€¦ (More)

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Mapping our universe in 3D by imaging the redshifted 21 cm line from neutralâ€¦ (More)

Monodisperse carbonaceous spheres produced by the hydrothermal carbonization of sucrose were first applied as green stationary phase for ion chromatography after quaternization. Depending on theâ€¦ (More)

A simple and rapid column-switching ion chromatography with non-suppressed conductivity detection method was developed for simultaneous determination of L-carnitine, choline and mineral ions (freeâ€¦ (More)

The harmonic index H(G) of a graph G is defined as the sum of weights 2 d(u) + d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we first present a sharpâ€¦ (More)