for any $k in mathbb{n}$, the $k$-subdivision of graph $g$ is a simple graph $g^{frac{1}{k}}$, which is constructed by replacing each edge of $g$ with a path of length $k$. in [moharram n. iradmusa, on colorings of graph fractional powers, discrete math., (310) 2010, no. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $g$ has been introduced as a fractional power of $g$, denoted by ...

in this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. weobserve that over a commutative ring $r$, $bbb{ag}_*(_rm)$ isconnected and diam$bbb{ag}_*(_rm)leq 3$. moreover, if $bbb{ag}_*(_rm)$ contains a cycle, then $mbox{gr}bbb{ag}_*(_rm)leq 4$. also for an $r$-module $m$ with$bbb{a}_*(m)neq s(m)setminus {0}$, $...

in this paper, some applications of our earlier results in working with chemical graphs arepresented.

an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

This paper presents a method for the recognition of object class once parts have been detected. The recognition task is formulated as a graph search problem in which the optimal score function is derived from Bayesian maximum a posteriori estimation. An efficient graph search algorithm is used to find the optimal solution. The method differs from previous approaches, such as one proposed by Bur...

Adapting a method developed for the study of quantum chaos on quantum (metric) graphs [1], spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph, and obtaining functions which belongs to the class of ζ functions proposed originally by Ihara [2], and expanded...

‎in this paper we introduce the concept of order difference interval graph $gamma_{odi}(g)$ of a group $g$‎. ‎it is a graph $gamma_{odi}(g)$ with $v(gamma_{odi}(g)) = g$ and two vertices $a$ and $b$ are adjacent in $gamma_{odi}(g)$ if and only if $o(b)-o(a) in [o(a)‎, ‎o(b)]$‎. ‎without loss of generality‎, ‎we assume that $o(a) leq o(b)$‎. ‎in this paper we obtain several properties of $gamma_...

let g be a fixed element of a finite group g. we introduce the g-noncommuting graph of g whose vertex set is whole elements of the group g and two vertices x,y are adjacent whenever [x,y] g  and  [y,x] g. we denote this graph by . in this paper, we present some graph theoretical properties of g-noncommuting graph. specially, we investigate about its planarity and regularity, its clique number a...

 The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$. In this paper, we study the connectivity and diameter of this  graph. Also we give a relation between the order graph and prime  graph of a group.

Let graph energy is a graph--spectrum--based quantity‎, ‎introduced in the 1970s‎. ‎After a latent period of 20--30 years‎, ‎it became a popular topic of research both‎ ‎in mathematical chemistry and in ``pure'' spectral graph theory‎, ‎resulting in‎ ‎over 600 published papers‎. ‎Eventually‎, ‎scores of different graph energies have‎ ‎been conceived‎. ‎In this article we...