The vertex distance complement (VDC) matrix \(\textit{C}\), of a connected graph \(G\) with set consisting \(n\) vertices, is real symmetric \([c_{ij}]\) that takes the value \(n - d_{ij}\) where \(d_{ij}\) between vertices \(v_i\) and \(v_j\) for \(i \neq j\) 0 otherwise. spectrum subdivision join, \(G_1 \dot{\bigvee} G_2\) edge join \underline{\bigvee} regular graphs \(G_1\) \(G_2\) in terms ...

Connection matrices for graph parameters with values in a field have been introduced by M. Freedman, L. Lovász and A. Schrijver (2007). Graph parameters with connection matrices of finite rank can be computed in polynomial time on graph classes of bounded tree-width. We introduce join matrices, a generalization of connection matrices, and allow graph parameters to take values in the tropical ri...

Evaluating Regular Path Queries (RPQs) have been of interest since they were used as a powerful way to explore paths and patterns in graph databases. Traditional automata-based approaches are restricted the size and/or highly complex queries, which causes high evaluation cost (e.g., memory space response time) on large graphs. Recently, although using approach based threshold rare label for gra...

In pursuit of graph processing performance, the systems community has largely abandoned general-purpose distributed dataflow frameworks in favor of specialized graph processing systems that provide tailored programming abstractions and accelerate the execution of iterative graph algorithms. In this paper we argue that many of the advantages of specialized graph processing systems can be recover...

In this paper, we investigate the concept of resolving dominating set in a graph. particular, characterize sets join, corona and lexicographic product two graphs determine domination number these graphs.

The growing popularity of graph databases has generated interesting data management problems, such as subgraph search, shortest-path query, reachability verification, and pattern match. Among these, a pattern match query is more flexible compared to a subgraph search and more informative compared to a shortest-path or reachability query. In this paper, we address pattern match problems over a l...

For a DBMS that provides support for a declarative query language like SQL, the query optimizer is a crucial piece of software. The declarative nature of a query allows it to be translated into many equivalent evaluation plans. The process of choosing a suitable plan from all alternatives is known as query optimization. The basis of this choice are a cost model and statistics over the data. Ess...

For an ordered set { } k w w w W , , , 2 1  = of vertices and a vertex v in a connected graph G, the (metric) representation of v with respect to W is the k-vector r(v/W) = (d(v, w1), d(v, w2), ..., d(v, wk)), where d(x, y)representsthe distance between the vertices x and y. A resolving set of minimum cardinality is called a minimum resolving set or abasis and the cardinality of a basis for G ...