Use the Spur dike as one of the easiest ways to protect the costal of the river has always been of interest to River engineers.The aim of this study was numerical investigate, the effect of distance and angle of the spur dikes parameters  on the pattern of distribution of average velocity  and the location of maximum velocity position at a mild 90 degree bend. For this purpose used ANSYS CFX so...

A graph H is strongly immersed in G if G is obtained from H by a sequence of vertex splittings (i.e., lifting some pairs of incident edges and removing the vertex) and edge removals. Equivalently, vertices of H are mapped to distinct vertices of G (branch vertices) and edges of H are mapped to pairwise edge-disjoint paths in G, each of them joining the branch vertices corresponding to the ends ...

The vertex arboricity of graph G is the minimum number of colors that can be used to color the vertices of G so that each color class induces an acyclic subgraph of G. We prove results such as this: if a connected graph G is neither a cycle nor a clique, then there is a coloring of V(G/ with at most [-A(G)/2 ~ colors, such that each color class induces a forest and one of those induced forests ...

We show that the intersection dimension of graphs with respect to several hereditary graph classes can be bounded as a function of the maximum degree. As an interesting special case, we show that the circular dimension of a graph with maximum degree ∆ is at most O(∆ log∆ log log∆). We also obtain bounds in terms of treewidth.

A graph H is a square root of a graph G if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2. The Square Root problem is that of deciding whether a given graph admits a square root. This problem is only known to be NP-complete for chordal graphs and polynomial-time solvable for non-trivial minor-closed graph classes and a very limited number of othe...