Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...

In this paper, we characterize line graphs and total graphs that are hinge-free, i.e., there is no triple of vertices x; y; z such that the distance between y and z increases after x is removed. Based on our characterizations, we show that given a graph G with n vertices and m edges, determining its line graph and total graph to be hinge-free can be solved in O(n + m) time. Moreover, characteri...

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...

Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...

the total version of geometric–arithmetic index of graphs is introduced based on the endvertexdegrees of edges of their total graphs. in this paper, beside of computing the total gaindex for some graphs, its some properties especially lower and upper bounds are obtained.

Let $G= (V,E)$ be a $(p,q)$-graph. A bijection $f: Eto{1,2,3,ldots,q }$ is called an edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ where $f^+(u) = sum_{uwin E} f(uw)$. Moreover, a bijection $f: Eto{1,2,3,ldots,q }$ is called a semi-edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ or $f^+(u)=f^+(v)$. A graph that admits an  ...

let $i$ be a proper ideal of a commutative semiring $r$ and let $p(i)$ be the set of all elements of $r$ that are not prime to $i$. in this paper, we investigate the total graph of $r$ with respect to $i$, denoted by $t(gamma_{i} (r))$. it is the (undirected) graph with elements of $r$ as vertices, and for distinct $x, y in r$, the vertices $x$ and $y$ are adjacent if and only if $x + y in p(i)...

given a graph $g$, the total dominator coloring problem seeks aproper coloring of $g$ with the additional property that everyvertex in the graph is adjacent to all vertices of a color class. weseek to minimize the number of color classes. we initiate to studythis problem on several classes of graphs, as well as findinggeneral bounds and characterizations. we also compare the totaldominator chro...

Soft set is a classification of elements the universe with respect to some given parameters. It new approach for modeling vagueness and uncertainty. The concept soft graph used provide parameterized point view graphs. In this paper we introduce concepts subdivision graph, power line investigate their properties.