‎let $g$ be a finite group which is not a cyclic $p$-group‎, ‎$p$ a prime number‎. ‎we define an undirected simple graph $delta(g)$ whose‎ ‎vertices are the proper subgroups of $g$, which are not contained in the‎ ‎frattini subgroup of $g$ and two vertices $h$ and $k$ are joined by an edge‎ ‎if and only if $g=langle h‎ , ‎krangle$‎. ‎in this paper we classify finite groups with planar graph‎. ‎...

A Join Index is a data structure that optimizes the join query processing in spatial databases. Join indices use pre-computation techniques to speed up online query processing and are useful for applications which require low update rates. The cost of spatial join computation using a join-index with limited buuer space depends primarily on the page access sequence used to fetch the pages of the...

The relational model is the most commonly used data model for storing large datasets, perhaps due to the simplicity of the tabular format which had revolutionized database management systems. However, many real world objects are recursive and associative in nature which makes storage in the relational model difficult. The hypergraph model is a generalization of a graph model, where each hyperno...

‎Let $G$ be a finite group which is not a cyclic $p$-group‎, ‎$p$ a prime number‎. ‎We define an undirected simple graph $Delta(G)$ whose‎ ‎vertices are the proper subgroups of $G$, which are not contained in the‎ ‎Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge‎ ‎if and only if $G=langle H‎ , ‎Krangle$‎. ‎In this paper we classify finite groups with planar graph‎. ‎...

The quadratic embedding constant (QE constant) of a graph is new characteristic value defined through the distance matrix. We derive formulae for QE constants join two regular graphs, double graphs and certain lexicographic product graphs. Examples include complete bipartite wheel friendship completely split graph, some associated to strongly

Graph has great expressive power to describe the complex relationships among data objects, and there are large graph datasets available. In this paper, we focus ourselves on processing a primitive graph query. We call it reachability query. The reachability query, denoted A D, is to find all elements of a type D that are reachable from some elements in another type A. The problem is challenging...

References [1] Leonidas Fegaras. A new heuristic for optimizing large queries. [2] Toshihide Ibaraki and Tiko Kameda. On the optimal nesting order for computing n-relational joins. Optimizing large join queries using a graph-based approach. [5] Guido Moerkotte and Thomas Neumann. Analysis of two existing and one new dynamic programming algorithm for the generation of optimal bushy join trees wi...

ÐAlthough many query tree optimization strategies have been proposed in the literature, there still is a lack of a formal and complete representation of all possible permutations of query operations (i.e., execution plans) in a uniform manner. A graph-theoretic approach presented in this paper provides a sound mathematical basis for representing a query and searching for an execution plan. In t...

A lot of real-life data are of graph nature. However, it is not until recently that business begins to exploit data’s connectedness for business insights. On the other hand, RDBMSs are a mature technology for data management, but they are not for graph processing. Take graph traversal, a common graph operation for example, it heavily relies on a graph primitive that accesses a given node’s neig...

Graph is a ubiquitous structure representing entities and their relationships applied in many areas such as social networks, web graphs, biological networks. One of the fundamental tasks graph analytics to investigate relations between two vertices (e.g., users, items, entities) how vertex A influences another B, or what extent B are similar each other, based on topology structure. For this pur...