Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by Γ′(R), is a graph with vertices in W ∗(R), which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in W ∗(R) are adjacent if and only if a / ∈ bR and b / ∈ aR. In this paper, we characterize all commutative rings whose cozero-divisor graphs are forest, star, doubl...

There is a natural graph associated to the zero-divisors of a commutative semiring with non-zero identity. In this article we essentially study zero-divisor graphs with respect to primal and non-primal ideals of a commutative semiring R and investigate the interplay between the semiring-theoretic properties of R and the graph-theoretic properties of ΓI(R) for some ideal I of R. We also show tha...

continue to investigate the problem of the existence of a Hamilton connected cubic (m,n)-metacirculant graphs. We show that a connected cubic (m,n)-metacirculant graph G = MC(m, n, a, So, ,.., has Hamilton cycle if either a 2 == 1 (mod n) or in the case of an odd number f.L one of the numbers (a 1) or a + a 2 _ ... ajJ.-2 + ajJ.-l) relatively to n. As a corollary of results we obtain that every...

We investigate, using purely combinatorial methods, structural and algorithmic properties of linear equivalence classes of divisors on tropical curves. In particular, an elementary proof of the RiemannRoch theorem for tropical curves, similar to the recent proof of the Riemann-Roch theorem for graphs by Baker and Norine, is presented. In addition, a conjecture of Baker asserting that the rank o...

It is known that isomorphisms of graph Jacobians induce cyclic bijections on the associated graphs. We characterize when such can be strengthened to isomorphisms, in terms an easily computed divisor. The result refines tools used algebraic geometry examine fibers compactified Torelli map.