Construction of (n+ 1) -dimensional dual-mode nonlinear equations: multiple shock wave solutions for (3 + 1) -dimensional dual-mode Gardner-type and KdV-type

The goal of this study is to offer an exclusive functional conversion to produce (n+ 1) -dimensional dual-mode nonlinear equations. This transformation has been implemented and new (3 + 1) -dimensional dual-mode Gradner-type and KdV-type have been established. Finally, the simplified bilinear method is used to tell the necessary conditions on these new models to have multiple singular-solitons. - 2019, The Author(s).This work is financially supported by UKM Grant: DIP-2017-011 and Ministry of Education Malaysia Grant FRGS/1/2017/STG06/UKM/01/1.Scopu

The basis number of the strong product of paths and cycles with bipartite graphs

The basis number of a graph G is defined to be the least integer d such that there is a basis B of the cycle space of G such that each edge of G is contained in at most d members of B. MacLane [13] proved that a graph G is planar if and only if the basis number of G is less than or equal to 2. Ali [3] proved that the basis number of the strong product of a path and a star is less than or equal to 4. In this work, (1) We give an appropriate decomposition of trees. (2) We give an upper bound of the basis number of a cycle and a bipartite graph. (3) We give an upper bound of the basis number of a path and a bipartite graph. This is a generalization of Ali's result [3].Scopu

A best proximity point theorem for special generalized proximal ?-quasi contractive mappings

In this paper, we obtain some best proximity point results for a new class of non-self mappings T: A? B called special generalized proximal ?-quasi contractive. Our result is illustrated by an example. Several consequences are derived. - 2019, The Author(s).Scopu

Edge Maximal C2k+1-edge Disjoint Free Graphs

For two positive integers r and s, G(n;r,s) denotes to the class of graphs on n vertices containing no r of s-edge disjoint cycles and f(n;r,s) = max{E(G):G ∈ G(n;r,s)}. In this paper, for integers r ≥ 2 and k ≥ 1, we determine f(n;r,2k+1) and characterize the edge maximal members in G(n;r,2k+1).Scopu

Extended rectangular b-metric spaces and some fixed point theorems for contractive mappings

In this paper, we introduce the class of extended rectangular b-metric spaces as a generalization of both rectangular metric and rectangular b-metric spaces. In addition, some fixed point results connected with certain contractions are obtained and examples are given to illustrate these results.Scopu

The theta-complete graph Ramsey number r(θk, K5); k = 7, 8, 9

Finding the Ramsey number is an important problem of the well-known family of the combinatorial problems in Ramsey theory. In this work, we investigate the Ramsey number r(θs, K5) for s = 7, 8, 9 where θs is the set of theta graphs of order s and K5 is a complete graph of order 5. Our result closed the problem of finding R(θs, K5) for each s ≥ 6.Scopu

On minimum cycle bases of the wreath product of wheels with stars

The length of a cycle basis of a graph is the sum of the lengths of its elements. A minimum cycle basis is a cycle basis with minimum length. In this work, a construction of a minimum cycle basis for the wreath product of wheels with stars is presented. Moreover, the length of minimum cycle basis and the length of its longest cycle are calculated.Scopu