Subgraph enumeration, which aims to find all the subgraphs of a large data graph that are isomorphic to a given pattern graph, is a fundamental graph problem with a wide range of applications. However, existing sequential algorithms for subgraph enumeration fall short in handling large graphs due to the involvement of computationally intensive subgraph isomorphism operations. Thus, some recent ...

We present a novel approach to implement a graph transformation engine based on standard relational database management systems (RDBMSs). The essence of the approach is to create database views for each rules and to handle pattern matching by inner join operations while negative application conditions by left outer join operations. Furthermore, the model manipulation prescribed by the applicati...

‎let $f$ be a proper $k$-coloring of a connected graph $g$ and‎ ‎$pi=(v_1,v_2,ldots,v_k)$ 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 $pi$ is defined to be the ordered‎ ‎$k$-tuple $c_{{}_pi}(v)=(d(v,v_1),d(v,v_2),ldots,d(v,v_k))$‎, ‎where $d(v,v_i)=min{d(v,x):~xin v_i}‎, ‎1leq ileq k$‎. ‎if‎ ‎distinct...

The complete double vertex graph $M_2(G)$ of $G$ is defined as the whose vertices are $2$-multisubsets $V(G)$, and two such adjacent in if their symmetric difference (as multisets) a pair $G$. In this paper we exhibit an infinite family graphs (containing Hamiltonian non-Hamiltonian graphs) for which Hamiltonian.

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

Let $G$ be a finite and simple graph with edge set $E(G)$‎. ‎The revised Szeged index is defined as‎ ‎$Sz^{*}(G)=sum_{e=uvin E(G)}(n_u(e|G)+frac{n_{G}(e)}{2})(n_v(e|G)+frac{n_{G}(e)}{2}),$‎ ‎where $n_u(e|G)$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$ and‎ ‎$n_{G}(e)$ is the number of‎ ‎equidistant vertices of $e$ in $G$‎. ‎In this paper...

This talk describes a new graph-pattern engine called Jedi.Using a recent simplification of worst-case optimal join al-gorithms due to Ngo et al., Jedi translates join queries intoa series of set intersection and union operations. Such setoperations are ideally suited to modern CPUs that providessingle-instruction, multiple data (SIMD) instructions. Usingthese ideas, we ...

‎Let $f$ be a proper $k$-coloring of a connected graph $G$ and‎ ‎$Pi=(V_1,V_2,ldots,V_k)$ 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 $Pi$ is defined to be the ordered‎ ‎$k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$‎, ‎where $d(v,V_i)=min{d(v,x):~xin V_i}‎, ‎1leq ileq k$‎. ‎If‎ ‎distinct...