To expand query types under a set of integrity constraints for obtaining consistent answers over inconsistent databases, a computational theory is proposed based on first-order logic. According to directed join graphs of queries and their join completeness, computational complexities of CQA are PTIME if query types are key-key, nonkey-key, incomplete key-key with acyclic join. This paper presen...

In the graph database literature the term “join” does not refer to an operator used to merge two graphs. In particular, a counterpart of the relational join is not present in existing graph query languages, and consequently no efficient algorithms have been developed for this operator. This paper provides two main contributions. First, we define a binary graph join operator that acts on the ver...

We characterize the class of infinite connected graphs G for which there exists a T -join for any choice of an infinite T ⊆ V (G). We also show that the following well-known fact remains true in the infinite case. If G is connected and does not contain a T -join, then it will if we either remove an arbitrary vertex from T or add any new vertex to T .

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....

Let f be a proper k-coloring of a connected graph G and Π = (V1, V2, . . . , Vk) be an ordered partition of V (G) into the resulting color classes. For a vertex v of G, the color code of v with respect to Π is defined to be the ordered k-tuple cΠ(v) = (d(v, V1), d(v, V2), . . . , d(v, Vk)), where d(v, Vi) = min{d(v, x) : x ∈ Vi}, 1 ≤ i ≤ k. If distinct vertices have distinct color codes, then f...

To support analytics on massive graphs such as online social networks, RDF, Semantic Web, etc. many new graph algorithms are designed to query graphs for a specific problem, and many distributed graph processing systems are developed to support graph querying by programming. A main issue to be addressed is how RDBMS can support graph processing. And the first thing is how RDBMS can support grap...

Let G = (V (G), E(G)) be a simple connected graph. A set S ⊆ V (G) is said to perfect isolate dominating of if and an G. The minimum cardinality called domination number, denoted by γp0(G). with |S| γp0(G) γp0-set. In this paper, the author gives characterization some graphs obtained from join, corona lexicographic product two graphs. Moreover, number forenamed determined also, having no are ex...