given a graph $g$, let $g^sigma$ be an oriented graph of $g$ with the orientation $sigma$ and skew-adjacency matrix $s(g^sigma)$. then the spectrum of $s(g^sigma)$ consisting of all the eigenvalues of $s(g^sigma)$ is called the skew-spectrum of $g^sigma$, denoted by $sp(g^sigma)$. the skew energy of the oriented graph $g^sigma$, denoted by $mathcal{e}_s(g^sigma)$, is defined as the sum of the n...

Abstract. In this paper, lexicographic products of two fuzzy graphs namely, lexicographic min-product and lexicographic max-product which are analogous to the concept lexicographic product in crisp graph theory are defined. It is illustrated that the operations lexicographic products are not commutative. The connected, effective and complete properties of the operations lexicographic products a...

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...

Many large graphs can be constructed from existing smaller graphs by using graph operations, for example, the Cartesian product and the lexicographic product. Many properties of such large graphs are closely related to those of the corresponding smaller ones. In this short note, we give some properties of the lexicographic products of vertextransitive and of edge-transitive graphs. In particula...

A linear ordering is said to be representable if it can be order-embedded into the reals. Representable linear orderings have been characterized as those which are separable in the order topology and have at most countably many jumps. We use this characterization to study the representability of a lexicographic product of linear orderings. First we count the jumps in a lexicographic product in ...