Now showing items 1-20 of 285

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

( Central Missouri State University , 2007 , Article)
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 ...
• #### The ramsey number for theta graph versus a clique of order three and four ﻿

( University of Zielona Gora , 2014 , Article)
For any two graphs F1 and F2, the graph Ramsey number r(F1, F2) is the smallest positive integer N with the property that every graph on at least N vertices contains F1 or its complement contains F2 as a subgraph. In ...
• #### The cycle-complete graph Ramsey number r(C6,K8)≤38 ﻿

( Tokyo University of Science , 2008 , Article)
The cycle-complete graph Ramsey number r ( C m , K n ) is the smallest integer N such that every graph G of order N contains a cycle C m on m vertices or has independent number α ( G ) ≥ n . ...
• #### The cycle-complete graph Ramsey number r ( C 8 , K 8 ) ﻿

( Tokyo University of Science , 2007 , Article)
The cycle-complete graph Ramsey number r ( C m , K n ) is the smallest integer N such that every graph G of order N contains a cycle C m on m vertices or has independent number α ( G ) ≥ n . ...
• #### The theta-complete graph Ramsey number r(θk, K5); k = 7, 8, 9 ﻿

( Forum-Editrice Universitaria Udinese SRL , 2021 , Article)
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 ...
• #### On the basis number and the minimum cycle bases of the wreath product of some graphs II ﻿

( University of Zielona Gora , 2010 , Article)
A construction of a minimum cycle bases for the wreath product of a star by a path, two stars and a star by a wheel is given. Moreover, the basis numbers of these products are determined.
• #### Minimum cycle bases for direct products of K2 with complete graphs ﻿

( University of Queensland Press , 2009 , Article)
We construct a minimum cycle basis for the direct product K2 x Kp of two complete graphs where p &gt; 2. For p &gt; 3, these bases consists only of squares. This completes the work of R. Hammack, who treated the case Kp x ...
• #### On the basis number of the wreath product of paths with wheels and some related problems ﻿

( Charles Babbage Research Centre , 2017 , Article)
In this paper, we investigate the basis number for the wreath product of wheels with paths. Also, as a related problem, we construct a minimum cycle basis of the same.
• #### On the sandpile model of modified wheels II ﻿

( De Gruyter Open Ltd , 2020 , Article)
: We investigate the abelian sandpile group on modified wheels Wˆn by using a variant of the dollar game as described in [N. L. Biggs, Chip-Firing and the critical group of a graph, J. Algebr. Comb. 9 (1999), 25–45]. The ...
• #### On minimum cycle bases of the wreath product of wheels with stars ﻿

( Zenodo , 2010 , Article)
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 ...
• #### Finite Element Analysis of the Dynamics of Power-Law Fluid around an Obstacle in a Channel ﻿

( Hindawi Limited , 2022 , Article)
Control of uid forces is an emerging area of research with numerous engineering applications. ­e uneven wake behind an obstacle causes undesirable structural oscillations, which can lead to fatigue or structural failure. ...
• #### Numerical investigation of dusty tri-hybrid Ellis rotating nanofluid flow and thermal transportation over a stretchable Riga plate ﻿

( Nature Research , 2023 , Article)
Due to high-ultra thermic significances, the nanosize materials are used in various chemical and mechanical engineering, modern technology and thermic engineering eras. For industrial growth of a country, one of the biggest ...
• #### Fundamental group and cycle space of dual graphs and applications ﻿

( Elsevier , 2010 , Article)
In this work, we study the fundamental group of dual graph of a planar graph. Moreover, we show that a planar graph G has no cut vertex if and only if N(Π(D(G))) = N(Π(D(G − v))) − 1 for any v ∈ V(G). Some applications ...
• #### Some α − ϕ-Fuzzy Cone Contraction Results with Integral Type Application ﻿

( Hindawi Limited , 2021 , Article)
In this paper, we define α-admissible and α-ϕ-fuzzy cone contraction in fuzzy cone metric space to prove some fixed point theorems. Some related sequences with contraction mappings have been discussed. Ultimately, our ...
• #### Optical solitons and qualitative analysis of nonlinear Schrodinger equation in the presence of self steepening and self frequency shift ﻿

( Elsevier , 2022 , Article)
In this manuscript, the optical solitons of nonlinear Schrödinger equation (NLSE) with cubic–quintic law nonlinearity, in the presence of self-frequency shift and self-steepening, has been studied. The ultrahigh capacity ...
• #### Exact traveling wave solutions for two prolific conformable M-Fractional differential equations via three diverse approaches ﻿

( Elsevier , 2021 , Article)
In this paper, we obtain the exact traveling solutions of the M-fractional generalized reaction Duffing model and density dependent M-fractional diffusion reaction equation by using three fertile, (G′ /G, 1/G), modified ...
• #### New solitary wave and computational solitons for Kundu-Eckhaus equation ﻿

( Elsevier , 2022 , Article)
The goal of this research is to find novel optical solutions to the Kundu-Eckhaus equation, which possess crucial roles in the field of nonlinear optics. A collective variable (CV) strategy is adopted to solve governing ...
• #### On Some Properties of Multiplicative Topological Indices in Silicon-Carbon ﻿

( Hindawi Limited , 2021 , Article)
)e use of graph theory can be visualized in nanochemistry, computer networks, Google maps, and molecular graph which are common areas to elaborate application of this subject. In nanochemistry, a numeric number (topological ...
• #### A new upper bound of the basis number of the lexicographic product of graphs ﻿

( Charles Babbage Research Centre , 2010 , Article)
An upper bound of the basis number of the lexicographic product of two graphs from the basis number of the factors is presented. Furthermore, the basis numbers of the lexicographic product of some classes of graphs is determined.
• #### Bifurcation of some new traveling wave solutions for the time-space M- fractional MEW equation via three altered methods ﻿

( Elsevier , 2022 , Article)
In this work,(1/G′ ), modified ( G′ /G2) and new extended direct algebraic methods are proposed to construct the novel exact traveling wave solutions in the form of trigonometric, hyperbolic and exponential functions ...