In this paper we study a convection–diffusion equation on star-shaped graph composed by n incoming edges and m outgoing with nonlinearity $$f\in C^1({\mathbb {R}})$$ satisfying some additional general conditions. First, prove the global well-posedness of solutions system under consideration. Next, in particular case that nonlinear convection is given $$\partial _x(f(u(t, x))$$ $$f(s)=-a|s|^{q-1...

A directed star forest is a forest all of whose components are stars with arcs emanating from the center to the leaves. The acircuitic directed star arboricity of an oriented graph G is the minimum number of edge-disjoint directed star forests whose union covers all edges of G and such that the union of two such forests is acircuitic. We show that graphs with maximum average degree less than 7 ...

The survival time T is the longest time that a virus, a meme, or a failure can propagate in a network. Using the hitting time of the absorbing state in an uniformized embedded Markov chain of the continuous-time susceptible-infected-susceptible (SIS) Markov process, we derive an exact expression for the average survival time E[T] of a virus in the complete graph K_{N} and the star graph K_{1,N-...

The aim of this work is to investigate the F-index and F-coindex of the line graphs of the cycle graphs, star graphs, tadpole graphs, wheel graphs and ladder graphs using the subdivision concepts. F-index of the line graph of subdivision graph of square grid graph, 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] are also investigated here.

In recent years, segmentation with graph cuts is increasingly used for a variety of applications, such as photo/video editing, medical image processing, etc. One of the most common applications of graph cut segmentation is extracting an object of interest from its background. If there is any knowledge about the object shape (i.e. a shape prior), incorporating this knowledge helps to achieve a m...

For a graph G, vertex v of G and integer r ≥ 1, we denote the family of independent r-sets of V (G) by I(r)(G) and the subfamily {A ∈ I(r)(G) : v ∈ A} by I v (G); such a subfamily is called a star. Then, G is said to be r-EKR if no intersecting subfamily of I(r)(G) is larger than the largest star in I(r)(G). If every intersecting subfamily of I v (G) of maximum size is a star, then G is said to...