Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.

1 PROBLEM DEFINITION The theory of bidimensionality provides general techniques for designing efficient fixed-parameter algorithms and approximation algorithms for a broad range of NP-hard graph problems in a broad range of graphs. This theory applies to graph problems that are " bidi-mensional " in the sense that (1) the solution value for the k ×k grid graph and similar graphs grows with k, t...

Game Graphs The model is based on a graph G = (S,E), consisting of a set S of states and a set E of directed edges between those states, the state transitions. We assume that every state has at least one outgoing edge. Figure 1(a) contains an example of such a graph representing a closed system where all indeterminism comes from the system itself (rather than from interaction with an outside en...

To a simple graph $G=(V,E)$, we correspond a simple graph $G_{triangle,square}$ whose vertex set is ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. The graph $G_{triangle,square}$ is called the $(triangle,square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the ...

The energy E(G) of a graph G is defined as the sum of the absolute values of the eigenvalues of G. An n-vertex graph is said to be hypoenergetic if E(G) < n and strongly hypoenergetic if E(G) < n−1. In this paper, we consider hypoenergetic and strongly hypoenergetic trees. For any given n, the existence of both hypoenergetic and strongly hypoenergetic trees of order n is completely characterized.

A subset S of the vertices of a directed acyclic graph is called glb-closed, if it contains the greatest lower bounds of all pairs of vertices of S. The glb-closure of S is the smallest glb-closed subset containing S. An eecient output sensitive algorithm for computing glb-closures is presented and two applications in the eld of object-oriented programming languages are discussed. 1 The problem...

In this paper, we propose a new mining task: mining top-k frequent closed graph patterns without minimum support. Most previous frequent graph pattern mining works require the specification of a minimum support threshold to perform the mining. However it is difficult for users to set a suitable value sometimes. We develop an efficient algorithm, called TGP, to mine patterns without minimum supp...

Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G − e; second, for all the vertices x of degree 3 in G− e, delete x from G− e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G a e. If G a...