the order graph of a group $g$, denoted by $gamma^*(g)$, is a graph whose vertices are subgroups of $g$ and two distinct vertices $h$ and $k$ are adjacent if and only if $|h|big{|}|k|$ or $|k|big{|}|h|$. in this paper, we study the connectivity and diameter of this  graph. also we give a relation between the order graph and prime  graph of a group.

let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...

in this paper, we first collect the earlier results about some graph operations and then wepresent applications of these results in working with chemical graphs.

Recently, complementary perfect corona domination in graphs was introduced. A dominating set S of a graph G is said to be (CPCD – set) if each vertex either pendent or support and has matching. The minimum cardinality called the number denoted by . In this paper, our parameter hasbeen discussed for power path cycle.

Broumi et al. [15] proposed the concept of interval-valued neutrosophic graphs. In this research article, we first show that there are some flaws in Broumi et al. [15] ’s definition, which cannot be applied in network models. We then modify the definition of an interval-valued neutrosophic graph. Further, we present some operations on interval-valued neutrosophic graphs. Moreover, we discuss th...

Inferring semantic relevance among entities (e.g., entries of Wikipedia) is important and challenging. According to the information resources, the inference can be categorized into learning with either raw text data, or labeled text data (e.g., wiki page), or graph knowledge (e.g, WordNet). Although graph knowledge tends to be more reliable, text data is much less costly and offers a better cov...

Querying large RDF spaces with traditional query languages such as SPARQL is challenging as it requires a familiarity with the structure of the RDF graph and the names (URIs) of its classes, properties and relevant individuals. In this paper, we propose a complementary approach based on Vector Space Models (VSM), more concretely Random Indexing (RI) [1] for building a semantic index for a large...

The Swap-Based Tabu Search (SBTS) is a heuristic algorithm for solving the maximum independent set problems and can solve clique as well because in graph equivalent to its complementary graph. Although SBTS powerful has abundant inherent parallelism, it difficult parallelize of solution searching involving indirect indexing on array components. In this paper, we show variant that does not requi...

An edge-operation on a graph G is defined to be either the deletion of an existing edge or the addition of a nonexisting edge. Given a family of graphs G, the editing distance from G to G is the smallest number of edge-operations needed to modify G into a graph from G. In this paper, we fix a graph H and consider Forb(n,H), the set of all graphs on n vertices that have no induced copy of H. We ...

We present a graph-based contour extraction algorithm for images with low contrast regions and faint contours. Our innovation consists of a new graph setup that exploits complementary information given by region segmentation and contour grouping. The information of the most salient region segments is combined together with the edge map obtained from the responses of an oriented filter bank. Thi...