The total graph is built by joining the to its line means of incidences. We introduce a similar construction for signed graphs. Under two defnitions graph, we defne corresponding and show that it stable under switching. consider balance, frustration index number, largesteigenvalue. In regular case compute spectrum adjacency matrix spectra certain compositions, determine some with exactly main e...

let $m$ be a module over a commutative ring $r$ and let $n$ be a proper submodule of $m$. the total graph of $m$ over $r$ with respect to $n$, denoted by $t(gamma_{n}(m))$, have been introduced and studied in [2]. in this paper, a generalization of the total graph $t(gamma_{n}(m))$, denoted by $t(gamma_{n,i}(m))$ is presented, where $i$ is an ideal of $r$. it is the graph with all elements of $...

let $r$ be a commutative ring and $m$ be an $r$-module with $t(m)$ as subset,   the set of torsion elements. the total graph of the module denoted   by $t(gamma(m))$, is the (undirected) graph with all elements of   $m$ as vertices, and for distinct elements  $n,m in m$, the   vertices $n$ and $m$ are adjacent if and only if $n+m in t(m)$. in this paper we   study the domination number of $t(ga...

Discussions about different graph Laplacians—mainly the normalized and unnormalized versions of graph Laplacian—have been ardent with respect to various methods of clustering and graph based semi-supervised learning. Previous research in the graph Laplacians, from a continuous perspective, investigated the convergence properties of the Laplacian operators on Riemannian Manifolds. In this paper,...

the main aim of this paper is to extend the recently developed methods for calculating the buckling loads of planar symmetric frames to include the effect of semi-rigidity of the joints. this is achieved by decomposing a symmetric model into two submodels and then healing them in such a manner that the ::::union:::: of the eigenvalues of the healed submodels result in the eigenvalues of the ent...

a vertex irregular total k-labeling of a graph g with vertex set v and edge set e is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...

Local algorithms for non-linear dimensionality reduction [1], [2], [3], [4], [5] and semi-supervised learning algorithms [6], [7] use spectral decomposition based on a nearest neighborhood graph. In the presence of shortcuts (union of two points whose distance measure along the submanifold is actually large), the resulting embbeding will be unsatisfactory. This paper proposes an algorithm to co...

Semi-supervised learning (SSL) provides a way to improve the performance of prediction models (e.g., classifier) via usage unlabeled samples. An effective and widely used method is construct graph that describes relationship between labeled Practical experience indicates quality significantly affects model performance. In this paper, we present visual analysis interactively constructs high-qual...

In this work‎, ‎we formulate Chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. We also discuss the uniqueness of the fixed point. The given result is a generalization of Chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a graph.