Motivated by questions concerning optical networks, in 2003 Gargano, Hammar, Hell, Stacho, and Vaccaro defined the notions of spanning spiders and arachnoid graphs. A spider is a tree with at most one branch (vertex of degree at least 3). The spider is centred at the branch vertex (if there is any, otherwise it is centred at any of the vertices). A graph is arachnoid if it has a spanning spider...

Textual database programming languages are computationally complete, but have the disadvantage of giving the user a non-intuitive view of the database information that is being manipulated. Visual languages developed in recent years have allowed naive users access to a direct representation of data, often in a graph form, but have concentrated on user interface rather than complex programming t...

We consider discrete-time birth-death chains on a spider, i.e. graph consisting of N discrete half lines the plane that are joined at origin. This process can be identified with quasi-birth-death state space N0×{1,2,…,N}, represented by block tridiagonal transition probability matrix. prove we analyze this using spectral methods and obtain n-step probabilities in terms weight matrix correspondi...

We study the maximum differential coloring problem, where the vertices of an n-vertex graph must be labeled with distinct numbers ranging from 1 to n, so that the minimum absolute difference between two labels of any two adjacent vertices is maximized. As the problem is NP-hard for general graphs [16], we consider planar graphs and subclasses thereof. We prove that the maximum differential colo...

In this paper, we propose a honeycomb mesh variation, called a spider web network. Assume that m and n are positive even integers with mP 4. A spider web network SWðm; nÞ is a 3-regular bipartite planar graph with bipartition C and D. We prove that the honeycomb rectangular mesh HREMðm; nÞ is a spanning subgraph of SWðm; nÞ. We also prove that SWðm; nÞ e is hamiltonian for any e 2 E and SWðm; n...

Spider webs feature advanced structural performance due to the evolutionary success of over more than 3 × 109 years, including lightweight design and exceptional mechanical properties. are appealing for bio-inspired since web designs serve multiple functions protection prey catching. However, high computational cost limited quantified properties render extensive spider studies challenging in pa...

Web applications appear as mazes to a user. Using a web browser, the user explores each web page without seeing the structure of the entire service. For a software tester, it would be convenient to have a map, in form of a graph, describing the functional topology of the service. In that way, it would be possible to analyse the possible paths which can be navigated to discover redundancies and ...

tarantulas have recently become as pets in most parts of the world that increased the probability of encountering emergency physicians with patients hurt with these spiders. their attacks usually do not cause general manifestation, however there are some case reports in this regard. here, a 40-year-old man was reported who was referred to the emergency department with severe periumbilical pain ...

Motivated by a problem in the design of optical networks, we ask when a graph has a spanning spider (subdivision of a star), or, more generally, a spanning tree with a bounded number of branch vertices. We investigate the existence of these spanning subgraphs in analogy to classical studies of Hamiltonicity.

This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computa-tionally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools...