In this article we give a new definition of direct product of two arbitrary fuzzy graphs. We define the concepts of domination and total domination in this new product graph. We obtain an upper bound for the total domination number of the product fuzzy graph. Further we define the concept of total α-domination number and derive a lower bound for the total domination number of the product fuzzy ...

We introduce fuzziness to conceptual knowledge processing by using linguistic variables instead of a two-valued representation. The attribute/object table for conceptual lattices holds fuzzy membership values rather than TRUE/FALSE entries and can be mapped into a graph of dependencies. From this graph implications can be extracted together with the method to compute truth values for the inferi...

A exible query model is presented for well-formed XML documents. Our approach relies on modeling XML documents as labeled graphs and selectively extending their structure by computing fuzzy estimates of the importance of the information they provide, at the gran-ularity of XML tags. The result of such an extension is a fuzzy labeled graph. Query results are subgraphs of this fuzzy labeled graph...

In this paper, the cobondage set and cobondage number bC(G) of a fuzzy graph G are defined. The upper bound of a fuzzy graph with p nodes is given as min(p − (1 + S(G)), S(G) + 1). The exact values of bC(G) for some standard fuzzy graphs are found. Some results on bC(G) are also discussed. A numerical example is also illustrated. AMS subject classification: 03E72, 05C40, 05C72.

In this paper, bondage and non-bondage set of a fuzzy graph are discussed. The bondage number b(G) and non-bondage number bn(G) of a fuzzy graph G are defined. The upper bound for both b(G) and bn(G) are given. Also some results on b(G) and bn(G) are discussed. The exact values of b(G) and bn(G) are determined for several classes of fuzzy graphs. AMS Subject Classification: 03E72, 05C40, 05C72

In this paper the questions of defining the optimum allocation of centers in fuzzy transportation networks are observed by the minimax criterion. It is supposed that the information received from the geographical information system is presented as a fuzzy graph. In this case the task of defining optimum allocation of the centers transforms into the task of defining the fuzzy set of graph bases....

Let D be a non-trivial simple t-design. For 1 ≤ s ≤ t, we generalize the concept of the incidence graph of D and construct a new bipartite regular graph Γ. We obtain that the edge-transitivity of the graph Γ is equivalent to the s-flag-transitivity of the design D. We then, for s = 2, classify the semisymmetric graphs among the graphs Γ constructed from biplanes and triplanes. Finally, we study...

We deal with the graph operator Pow2 defined to be the complement of the square of a graph: Pow2(G) = Pow2(G). Motivated by one of many open problems formulated in [6] we look for graphs that are 2-periodic with respect to this operator. We describe a class G of bipartite graphs possessing the above mentioned property and prove that for any m,n ≥ 6, the complete bipartite graph Km,n can be deco...

In 2007, Levstein and Maldonado computed the Terwilliger algebra of the Johnson graph J(n,m) when 3m 6 n. It is well known that the halved graphs of the incidence graph J(n,m,m + 1) of Johnson geometry are Johnson graphs. In this paper, we determine the Terwilliger algebra of J(n,m,m + 1) when 3m 6 n, give two bases of this algebra, and calculate its dimension.

network sensors consist of sensor nodes in which every node covers a limited area. the most common use ofthese networks is in unreachable fields.sink is a node that collects data from other nodes.one of the main challenges in these networks is the limitation of nodes battery (power supply). therefore, the use oftopology control is required to decrease power consumption and increase network acce...