Connected sum and trivalent vertex are natural operations on genus 2 spatial graphs and, as with knots, tunnel number behaves in interesting ways under these operations. We prove sharp Scharlemann-Schultens type bounds for the of a composite graph. For Brunnian $\theta$-curve, our result implies that is at least summands, knot case. also version theorem Morimoto knots: m-small graph numbers fac...

A composite object represented as a directed graph is an important data structure which requires efficient support in CAD/CAM, CASE, office systems, software management, Web databases and document databases. It is cumbersome to handle such an object in relational database systems when it involves recursive relationships. In this chapter, we present a new encoding method to support the efficient...

The Distributed Constraint Optimization Problem (DCOP) offers a powerful approach for the description and resolution of cooperative multi-agent problems. In this model, a group of agents coordinates their actions to optimize a global objective function, taking into account their local preferences. In the majority of DCOP algorithms, agents operate on three main graphical representations of the ...

Directed graphs are a foundation for the encoding of various formal objects, such as requirement specifications and proof trees, in logic-based software synthesis and automated proving. The visualization of these objects by graph drawing can make formal descriptions more comprehensible and user-friendly. In this paper, we sketch and apply a distributed architecture with a World-Wide-Web user in...

In this Letter, we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph ...

The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we give formula for Merrifield-Simmons and Hosoya indices of some classes of cartesian product of two graphs K{_2}×H, where H is a path graph P{_n}, cyclic graph C{_n}, or star gra...

‎in this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $c_4$-free.‎

Complex nongradual evolutionary processes such as gene remodeling are difficult to model, to visualize, and to investigate systematically. Despite these challenges, the creation of composite (or mosaic) genes by combination of genetic segments from unrelated gene families was established as an important adaptive phenomena in eukaryotic genomes. In contrast, almost no general studies have been c...

The composite service design modeling is an essential process of the service-oriented software development life cycle, where the candidate services, composite services, operations and their dependencies are required to be identified and specified before their design. However, a systematic service-oriented design modeling method for composite services is still in its infancy as most of the exist...

a graph is called textit{circulant} if it is a cayley graph on a cyclic group, i.e. its adjacency matrix is circulant. let $d$ be a set of positive, proper divisors of the integer $n>1$. the integral circulant graph $icg_{n}(d)$ has the vertex set $mathbb{z}_{n}$ and the edge set e$(icg_{n}(d))= {{a,b}; gcd(a-b,n)in d }$. let $n=p_{1}p_{2}cdots p_{k}m$, where $p_{1},p_{2},cdots,p_{k}$ are disti...