the notion of strong arcs in a fuzzy graph was introduced bybhutani and rosenfeld in [1] and fuzzy end nodes in the subsequent paper[2] using the concept of strong arcs. in mordeson and yao [7], the notion of“degrees” for concepts fuzzified from graph theory were defined and studied.in this note, we discuss degrees for fuzzy end nodes and study further someproperties of fuzzy end nodes and fuzz...

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...

The Laplacian energy of a graph sums up the absolute values of the differences of average degree and eigenvalues of the Laplace matrix of the graph. This spectral graph parameter is upper bounded by the energy obtained when replacing the eigenvalues with the conjugate degree sequence of the graph, in which the i-th number counts the nodes having degree at least i. Because the sequences of eigen...

Let G be a graph of order n with Laplacian spectrum μ1 ≥ μ2 ≥ · · · ≥ μn. The Laplacian-energy-like invariant of graph G, LEL for short, is defined as: LEL(G) = n−1 ∑ k=1 √ μk . In this note, the extremal (maximal and minimal) LEL among all the connected graphs with given matching number is determined. The corresponding extremal graphs are completely characterized with respect to LEL. Moreover ...

Let G be a graph of order n with Laplacian spectrum μ1 ≥ μ2 ≥ · · · ≥ μn. The Laplacian-energy-like invariant of graph G, LEL for short, is defined as: LEL(G) = n−1 ∑ k=1 √ μk . In this note, the extremal (maximal and minimal) LEL among all the connected graphs with given matching number is determined. The corresponding extremal graphs are completely characterized with respect to LEL. Moreover ...

Matroids are important combinatorial structures and connect close-lywith graphs. Matroids and graphs were all generalized to fuzzysetting respectively. This paper tries to study  connections betweenfuzzy matroids and fuzzy graphs. For a given fuzzy graph, we firstinduce a sequence of matroids  from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matro...

This paper studies the problem of fault detection and isolation (FDI) for multi-agent systems (MAS) via complex Laplacian subject to actuator faults. A planar formation of point agents in the plane using simple and linear interaction rules related to complex Laplacian is achieved. The communication network is a directed, and yet connected graph with a fixed topology. The loss of symmetry in the...

In many real world problems, data sometimes comes from n agents (n≥2), multipolar information exists. For issues that are associated with uncertainty, this information can not be showed with the values of crisp, fuzzy, intuitionistic or bipolar. Graph is one of the mathematical models widely used in different sciences. Ambiguity in a graph where data depends on the n parameter can not be showed...

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...