Introduction. The line-graph L(G) of a nonempty graph G is the graph whose point set can be put in one-to-one correspondence with the line set of G in such a way that two points of L(G) are adjacent if and only if the corresponding lines of G are adjacent. In this paper graphs whose line-graphs are eulerian or hamiltonian are investigated and characterizations of these graphs are given. Further...

Let Γ be a simple graph of size m and degree sequence δ1 ≥ δ2 ≥ · · · ≥ δn. Let L(Γ) denotes the line graph of Γ. The aim of this paper is to study mathematical properties of the alliance number, a(L(Γ), and the global alliance number, γa(L(Γ)), of the line graph of a simple graph. We show that ⌈

We propose a method for computing acute (non-obtuse) triangulations. That is, for a given two dimensional domain (a set of points or a planar straight line graph), we compute a triangulation of the domain such that all angles are less than (or less than or equal to) π/2. This leads to the first software to compute such triangulations.

We treat zeta functions and complexities of semiregular bipartite graphs. Furthermore, we give formulas for zeta function and the complexity of a line graph of a semiregular bipartite graph. As a corollary, we present the complexity of a line graph of a complete bipartite graph. © 2006 Elsevier B.V. All rights reserved.

We show that the maximum number of convex polygons in a triangulation of n points in the plane is O(1.5029). This improves an earlier bound of O(1.6181) established by van Kreveld, Löffler, and Pach (2012) and almost matches the current best lower bound of Ω(1.5028) due to the same authors. Given a planar straight-line graph G with n vertices, we also show how to compute efficiently the number ...

For any planar straight line graph (Pslg), there is a vertexface assignment such that every vertex is assigned to at most two incident faces, and every face is assigned to all its reflex vertices and one more incident vertex. The existence of such an assignment implies, in turn, that any Pslg can be augmented to a connected Pslg such that the degree of every vertex increases by at most two.

It is shown that every connected planar straight line graph with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar straight line graph with at most b(2n − 2)/3c new edges. It is also shown that every planar straight line tree with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar topological graph by adding at most bn/2c edge...

A graph G is 1-Hamilton-connected if G − x is Hamilton-connected for every vertex x ∈ V (G). In the paper we introduce a closure concept for 1-Hamiltonconnectedness in claw-free graphs. If G is a (new) closure of a claw-free graph G, then G is 1-Hamilton-connected if and only if G is 1-Hamilton-connected, G is the line graph of a multigraph, and for some x ∈ V (G), G − x is the line graph of a ...

The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...