A bipartite graph G is called (α, β)-biregular if all vertices in one part of G have the degree α and all vertices in the other part have the degree β. An edge coloring of a graph G with colors 1, 2, 3, . . . , t is called an interval t-coloring if the colors received by the edges incident with each vertex of G are distinct and form an interval of integers and at least one edge of G is colored ...

Let S be a semiring and let Z(S)∗ be its set of nonzero zero divisors. We denote the zero divisor graph of S by Γ(S) whose vertex set is Z(S)∗ and there is an edge between the vertices x and y (x 6= y) in Γ(S) if and only if either xy = 0 or yx = 0. In this paper we study the zero divisor graph of the semiring of matrices Mn(B), (n > 1) over the Boolean semiring B. We investigate the properties...

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count n and a set D of divisors of n in such a way that they have vertex set Zn and edge set {{a, b} : a, b ∈ Zn, gcd(a− b, n) ∈ D}. Using tools from convex optimization, we study the maxim...

A simple graphoidal cover of a semigraph is such that any two paths in have atmost one end vertex common. The minimum cardinality called the covering number and denoted by . acyclic an In this paper we find for wheel semigraph, unicycle zero-divisor graph.

We introduce two exotic lattice models on a general spatial graph. The first one is matter theory of compact Lifshitz scalar field, while the second certain rank-2 $U(1)$ gauge fractons. Both are defined via discrete Laplacian operator unveil an intriguing correspondence between physical observables these and graph quantities. For instance, ground state degeneracy equals number spanning trees g...

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.

Let G be a finite group acting faithfully on an irreducible non-singular projective curve defined over an algebraically closed field F . Does every G-invariant divisor class contain a Ginvariant divisor? The answer depends only on G and not on the curve. We answer the same question for degree 0 divisor (classes). We investigate the question for cycles on varieties.