The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $\pi:V(G)\longrightarrow \{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. In this paper, we compute the packing chromatic number for enhanced hypercubes.
An elementary circuit (or \emph{tie}) is a subgraph of a graph and the set of edges in this subgraph is called an \emph{elementary tieset}. The \emph{distance} $d(e_{i}, e_{j})$ between two edges in an undirected graph is defined as the minimum number of edges in a tieset containing $e_{i}$ and $e_{j}$. The \emph{eccentricity} $\varepsilon_{\tau}(e_{i})$ of an edge $e_{i}$ is $\varepsilon_{\tau}(e_{i})=\displaystyle \max_{\substack{e_{j}\in E}}d(e_{i}, e_{j})$. In this paper, we have introduced the edge - self centered and edge - eccentric graph of a graph and have obtained results on these concepts.
The aim of this paper is to prove some common fixed point theorems for four mappings satisfying $(\psi,\varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give two examples to illustrate our results.
In the present paper, we prove a coupled coincidence fixed point theorem in the setting of two pairs of mappings in G-metric space. The main result is illustrated by an example.
In this paper, the reflection and transmission phenomenon at the imperfect interface between viscoelastic solid half space and elastic solid half space is presented. P-wave or SV-wave is considered to be incident on the interface through viscoelastic solid half space. The amplitude ratios of various reflected and transmitted waves to that of incident wave are derived and deduced for normal force stiffness, transverse force stiffness and for welded contact. After obtaining the amplitude ratios, they have been computed numerically for a particular model and results thus obtained are depicted graphically with angle of incidence of incident wave. It is found that these amplitude ratios depend on angle of incidence of the incident wave and material properties of the medium and these are affected by the stiffness also.
In this paper, an attempt has been made to study status of mathematical education at degree level in West Bengal, India. For this study, descriptive research design- normative survey research method has been applied on four degree colleges including one women's college under different universities of West Bengal. The findings of the analysis of survey data have been presented.
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