Planarity of Eccentric Digraphs of graphs

The eccentricity e(u) of a vertex u is the maximum distance of u to any othervertex of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a graph(digraph) G is thedigraph that has the same vertex set as G and an arc from u to v exists in ED(G) if and only if v is an eccentric vertex of u in G. In this paper, we consider planarity of eccentric digraph of a graph

Products and Eccentric digraphs

The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertex of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a graph(digraph) G is the digraph that has the same vertex as G and an arc from u to v exists in ED(G) if and only if v is an eccentric vertex of u in G. In this paper, we consider the eccentric digraphs of different products of graphs, viz., cartesian, normal, lexicographic, prism, et

Eccentric Coloring in graphs

he \emph{eccentricity} $e(u)$ of a vertex $u$ is the maximum distance of $u$ to any other vertex of $G$. A vertex $v$ is an \emph{eccentric vertex} of vertex $u$ if the distance from $u$ to $v$ is equal to $e(u)$. An \emph{eccentric coloring} of a graph $G = (V, E)$ is a function \emph{color}: $V \rightarrow N$ such that\\ (i) for all $u, v \in V$, $(color(u) = color(v)) \Rightarrow d(u, v) > color(u)$.\\ (ii) for all $v \in V$, $color(v) \leq e(v)$.\\ The \emph{eccentric chromatic number} $\chi_{e}\in N$ for a graph $G$ is the lowest number of colors for which it is possible to eccentrically color \ $G$ \ by colors: $V \rightarrow \{1, 2, \ldots , \chi_{e} \}$. In this paper, we have considered eccentric colorability of a graph in relation to other properties. Also, we have considered the eccentric colorability of lexicographic product of some special class of graphs

Products and Eccentric Diagraphs

The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertex of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a graph(digraph) G is the digraph that has the same vertex as G and an arc from u to v exists in ED(G) if and only if v is an eccentric vertex of u in G. In this paper, we consider the eccentric digraphs of different products of graphs, viz., cartesian, normal, lexicographic, prism, etc

On Edge-Distance and Edge-Eccentric graph of a graph

An elementary circuit (or tie) is a subgraph of a graph and the set of edges in this subgraphis called an elementary tieset. The distance d(ei, ej ) between two edges in an undirected graph is defined as the minimum number of edges in a tieset containing ei and ej . The eccentricity ετ (ei) of an edge ei is ετ (ei) = maxej∈Ed(ei, ej ). In this paper, we have introduced the edge - self centered and edge - eccentric graph of a graph and have obtained results on these concepts

Embedding in Distance Degree Regular and Distance Degree Injective graphs

The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertex of G.The distance degree sequence (dds) of a vertex u in a graph G = (V, E) is a list of the number of vertices at distance 1, 2,. . . , e(u) in that order, where e(u) denotes the eccentricity of u in G. Thus the sequence (di0 , di1 , di2 , . . . , dij , . . .) is the dds of the vertex vi in G where dij denotes number of vertices at distance j from vi . A graph is distance degree regular (DDR) graph if all vertices have the same dds. A graph is distance degree injective (DDI) graph if no two vertices have the same dds. In this paper, we consider the construction of a DDR graph having any given graph G as its induced subgraph. Also we consider construction of some special class of DDI graphs. Keywords: Distance degree sequence, Distance degree regular (DDR) graphs, Almost DDR graphs, Distance degree injective(DDI) grap

Products of distance degree regular and distance degree injective graphs.

The eccentricity e (u) of a vertex u is the maximum distance of u to any other vertex in G. The distance degree sequence (dds) of a vertex v in a graph G = (V, E) is a list of the number of vertices at distance 1, 2, …, e (u) in that order, where e (u) denotes the eccentricity of u in G. Thus the sequence is the dds of the vertex vi in G where denotes number of vertices at distance j from Vi . A graph is distance degree regular (DDR) graph if all vertices have the same dds. A graph is distance degree injective (DDI) graph if no two vertices have same dds. In this paper we consider Cartesian and normal products of DDR and DDI graphs. Some structural results have been obtained along with some characterizations

Performance Analysis of Switches in High Speed LAN

© ASEE 2009This paper presents an analysis of switches in high speed LAN. In order to support our analysis, this paper provides both analytical and mathematical models. The proposed analytical model is based on a finite state Markov model developed for analyzing networks with virtual channels in a switched LAN. Our proposed mathematical model provides a mean to quantify different critical parameters such as end-to-end delay, short and long message latency, channel bandwidth, and utilization in switched LAN. Simulation is performed using OPNET that based on the mathematical expressions derived in the mathematical model. In addition, simulation results of this paper compare the performance of high speed LAN with respect to the utilization of both switches and hub. Finally, based on the simulation results, we provide a performance analysis that indicates the role of each critical parameter in the overall perfor

Wear mechanism of olivine at the small-scale: An in situ TEM study

The study of tribology includes wear, friction, and lubrication of interacting surfaces in relative motions. Since the function, efficiency, and lifetime of many engineering components depend on the appropriate friction and wear properties, the study of tribology has significant practical importance. However, traditional tribology tests are limited by the inability to observe real-time progress of the sliding contacts and wear mechanism. Recent developments in small-scale devices, particularly piezoelectric and MEMS-based actuators, aid in conducting scratches at the micro- and nano-scale in the TEM. Olivine is magnesium iron silicate (Mg²⁺, Fe²⁺)₂SiO₄ and the most abundant mineral in earth\u27s upper mantle, which comprises the bulk of the planet\u27s tectonic plates. Although the structure of olivine has been intensively studied by mineralogists and geophysicists, the frictional and mechanical properties particularly damage evolution at the small-scale of sliding contact is unknown. In this study, a bulk olivine sample was wedge polished and then fib-milled to prepare electron-transparent regions. A wedge diamond indenter of 100 nm radius and 3 um length was used to make sliding contact using a PI 95, TEM PicoIndenter. Multicycle scratch tests were conducted to understand wear behavior. During the wear passes, the kinetic friction coefficient remained relatively constant near 0.1 and substantial dislocation plasticity occurred in the sample. Each pass showed nucleation of additional dislocations which were arranged in a symmetric array along the wear path as shown in fig. 1. The talk will present a theory of friction and deformation behavior that are applicable to geological materials. Please click Additional Files below to see the full abstract

Integration of TTF, UTAUT, and ITM for mobile Banking Adoption

The introduction of mobile banking facility has enabled customers to carry out banking transactionswith the use of smartphones and other handheld devices from anywhere. It has become a luxurious and exclusive method of online payments. The recent growth of telecommunication sector and a tremendous increase in mobile USAge has opened new doors for sparking future of banking sector industry. The following research is aimed to find out the mobile banking adoption attitudes with the integration of TTF, UTAUT,and ITM models