Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two character­ izations of decomposable models in terms of independence relationships, we develop an exact algorithm for recovering the chordal graphical representation of any given decom­ posable model. We also propose an algorithm for le...

Let G be a digraph with n vertices and A(G) be its adjacency matrix. A monic polynomial f(x) of degree at most n is called an annihilating polynomial of G if f(A(G)) = 0. G is said to be annihilatingly unique if it possesses a unique annihilating polynomial. In this paper, the directed windmill M3(r) is defined and we study the annihilating uniqueness of M3(r).

We associate two modules, the \(G\)-parking critical module and toppling module, to an undirected connected graph \(G\). The are canonical modules (with suitable twists) of quotient rings well-studied function ideal ideal, respectively. For each we establish a Tutte-like short exact sequence relating associated \(G\), edge contraction \(G/e\) deletion \(G \setminus e\) (\(e\) is non-bridge). ob...

In this paper, two classes of exact analytic time-dependent soultion of magnetic annihilation for incompressible magnetic fluid, have been obtained by solving the magnetohydro-dynamic (MHD) equations directly. The solutions derived here possess scaling property with time t as the scale factor. Based on these two solutions, we find that, for some given inflow fields, the evolution of the annihil...

Let R be a commutative ring and G(R) be a graph with vertices as proper andnon-trivial ideals of R. Two distinct vertices I and J are said to be adjacentif and only if I + J = R. In this paper we study a graph constructed froma subgraph G(R)Δ(R) of G(R) which consists of all ideals I of R such thatI Δ J(R), where J(R) denotes the Jacobson radical of R. In this paper westudy about the relation b...

‎In this paper‎, ‎exact formulas for the dependence‎, ‎independence‎, ‎vertex cover and clique polynomials of the power graph and its‎ ‎supergraphs for certain finite groups are presented‎.

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...