Graphs are typically visualized as node-link diagrams. Although there is a fair amount of research focusing on crossing minimization to improve readability, little attention has been paid on how to handle crossings when they are an essential part of the final visualizations. This requires us to understand how people read graphs and how crossings affect reading performance. As an initial step to...

A dominating set of a graph G is a set D of vertices of G such that every vertex outside D is adjacent to a vertex in D. A locating-dominating set of G is a dominating set D of G with the additional property that every two distinct vertices outside D have distinct neighbors in D; that is, for distinct vertices u and v outside D, N(u) ∩ D 6= N(v) ∩ D where N(u) denotes the open neighborhood of u...

Graphs are typically visualized as node-link diagrams. Although there is a fair amount of research focusing on crossing minimization to improve readability, little attention has been paid on how to handle crossings when they are an essential part of the final visualizations. This requires us to understand how people read graphs and how crossings affect reading performance. As an initial step to...

a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

Resources available over the Web are often used in combination to meet a specific need of a user. Since resource combinations can be represented as graphs in terms of the relations among the resources, locating desirable resource combinations can be formulated as locating the corresponding graph. This paper describes a graph clustering method based on structural similarity of fragments (current...

the center (periphery) of a graph is the set of vertices with minimum (maximum)eccentricity. in this paper, the structure of centers and peripheries of some classes ofcomposite graphs are determined. the relations between eccentricity, radius and diameterof such composite graphs are also investigated. as an application we determinethe center and periphery of some chemical graphs such as nanotor...

Consider a matrix valued function A(x) ∈ R, m ≥ n, smoothly depending on parameters x ∈ Ω ⊂ R, where Ω is simply connected and bounded. We consider a technique to locate parameter values where some of the q dominant (q ≤ n) singular values of A coalesce, in the specific case when A is large and m > n ≫ q. Notation. An m × n real matrix is indicated with A ∈ Rm×n. We always consider the 2-norm f...

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...

the degree kirchhoff index of a connected graph $g$ is defined as‎ ‎the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices‎, ‎where $d_i$ is the‎ ‎degree of the $i$-th vertex‎, ‎and $r_{ij}$ the resistance distance between the $i$-th and‎ ‎$j$-th vertex of $g$‎. ‎bounds for the degree kirchhoff index of the line and para-line‎ ‎graphs are determined‎. ‎the special case of regular grap...