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...

So far, we have been adopting the usual approach to spectral graph theory: understand graphs via the eigenvectors and eigenvalues of associated matrices. For example, given a graph G = (V,E), we defined an adjacency matrix A and considered the eigensystem Av = λv, and we also defined the Laplacian matrix L = D−A and considered the Laplacian quadratic form xTLx− ∑ (ij)∈E(xi−xj). There are other ...

In this paper, we obtain some upper and lower bounds for the general extended energy of a graph. As an application, we obtain few bounds for the (edge) Zagreb energy of a graph. Also, we deduce a relation between Zagreb energy and edge-Zagreb energy of a graph $G$ with minimum degree $delta ge2$. A lower and upper bound for the spectral radius of the edge-Zagreb matrix is obtained. Finally, we ...

this article proposes an optimization model for preventing the waste of time in the educational and research activities' cycle of an organization such as a university. for this purpose and in order to increase efficiency and prevent the waste of time; the graph theory models have been used. the educational and research activities diagrams of a supposed university is drawn by the use of graphs t...

Abstract In this paper, we use graph theory to solve wave scattering problems in the discrete dipole approximation. As a key result of work, presence active scatterers, present systematic method find arbitrary large-order zero eigenvalue exceptional points (EPs). This is achieved by solving set non-linear equations that interpret, picture, as vanishing sums events. We then show how total field ...

An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster graphs and then Randic computed complexit...

let $r$ be a ring with unity. the undirected nilpotent graph of $r$, denoted by $gamma_n(r)$, is a graph with vertex set ~$z_n(r)^* = {0neq x in r | xy in n(r) for some y in r^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in n(r)$, or equivalently, $yx in n(r)$, where $n(r)$ denoted the nilpotent elements of $r$. recently, it has been proved that if $r$ is a left ar...