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...

the rings considered in this article are  commutative  with identity which admit at least two  nonzero annihilating ideals. let $r$ be a ring. let $mathbb{a}(r)$ denote the set of all annihilating ideals of $r$ and let $mathbb{a}(r)^{*} = mathbb{a}(r)backslash {(0)}$. the annihilating-ideal graph of $r$, denoted by $mathbb{ag}(r)$  is an undirected simple graph whose vertex set is $mathbb{a}(r)...

Digital image processing is a subset of the electronic domain, wherein the image is converted to an array of small integers, called pixels, representing a physical quantity. Edges characterize boundaries and edge detection is one of the most difficult tasks in image processing hence it is a problem of fundamental importance in image processing. The problem of edge detection although it is funda...

‎let $g$ be a graph and $chi^{prime}_{aa}(g)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $g$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ‎we prove a general bound for $chi^{prime}_{aa}(gsquare h)$ for any two graphs $g$ and $h$‎. ‎we also determine‎ ‎exact value of this parameter for the cartesian product of ...

This abstract is essentially taken from the introduction of the paper Monomial and toric ideals associated to Ferrers graphs [13], written jointly with Alberto Corso. A Ferrers graph is a bipartite graph on two distinct vertex sets X = {x1, . . . , xn} and Y = {y1, . . . , ym} such that if (xi, yj) is an edge of G, then so is (xp, yq) for 1 ≤ p ≤ i and 1 ≤ q ≤ j. In addition, (x1, ym) and (xn, ...

We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. also provide examples oriented graphs that have non-Cohen-Macaulay vertex-weighted ideals, while the ideal their underlying graph is Cohen-Macaulay. This disproves a conjecture posed by Pitones, Reyes, Toledo.

The charged surfaces of micaceous minerals, especially illite, regulate the mobility of the major radioisotopes of Cs (134Cs, 135Cs, 137Cs) in the geosphere. Despite the long history of Cs adsorption studies, the nature of the illite surface sites remains incompletely understood. To address this problem, we present atomistic simulations of Cs competition with Na for three candidate illite adsor...