In this paper we introduce two new operations on graphs: sum and union corresponding to parallel and series operation respectively. We determine N-free graph as the graph that does not embed Necklace 4. We define “fin RelStr” as the set of all graphs with finite carriers. We also define the smallest class of graphs which contains the one-element graph and which is closed under parallel and seri...

In computer science, dependence analysis determines whether or not it is safe to parallelize statements in programs. In dealing with the data-intensive and computationally intensive spatial operations in processing massive volumes of geometric features, this dependence can be well utilized for exploiting the parallelism. In this paper, we propose a graph-based divide and conquer method for para...

Real life data can often be modeled as graphs, in which nodes represent objects and edges between nodes indicate their relationships. Large graph datasets are common in many emerging applications. Examples span from social networks, biological networks to computer networks. To fully exploit the wealth of information encoded in graphs, systems for managing and analyzing graph data are critical. ...

Graph grammars and graph transformation systems [9] have turned out to be applicable for solving various problems of recent computer science [3][4]. It is also known, however, that pure graph grammars are often no suitable solutions for practical problems, because graph grammar derivations (as any grammar derivations) are of non-deterministic nature whilst deterministic and predictable behavior...

In this paper, using a standard method of computing the chromatic polynomial of hypergraphs, we introduce a new reduction theorem which allows us to find explicit formulae for the chromatic polynomials of some (complete) non-uniform (m, l)− hyperwheels and non-uniform (m, l)−hyperfans. These hypergraphs, constructed through a “join” graph operation, are some generalizations of the well-known wh...

Here we investigate how the spectrum of the normalized graph Laplacian gets affected by certain graph operations like motif duplication and graph (or motif) joining.

In this paper, we define duplication corona, duplication neighborhood corona and duplication edge corona of two graphs. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs.

let $g=(v,e)$ be a connected graph. the eccentric connectivity index of $g$, $xi^{c}(g)$, is defined as $xi^{c}(g)=sum_{vin v(g)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. the eccentric distance sum of $g$ is defined as $xi^{d}(g)=sum_{vin v(g)}ec(v)d(v)$, where $d(v)=sum_{uin v(g)}d_{g}(u,v)$ and $d_{g}(u,v)$ is the distance between $u$ and $v$ ...