DM
2002
14 years 2 months ago
2002
We consider a variation of the chip-firing game in a induced subgraph S of a graph G. Starting from a given chip configuration, if a vertex v has at least as many chips as its deg...
JGT
2007
14 years 2 months ago
2007
: Let G be a graph with maximum degree d ≥ 3 and ω(G) ≤ d, where ω(G) is the clique number of the graph G. Let p1 and p2 be two positive integers such that d = p1 + p2. In th...
JCT
2007
14 years 2 months ago
2007
An induced subgraph is called homogeneous if it is either a clique or an independent set. Let hom(G) denote the size of the largest homogeneous subgraph of a graph G. In this shor...
JCT
2007
14 years 2 months ago
2007
Let P(G,t) and F(G,t) denote the chromatic and flow polynomials of a graph G. D.R. Woodall has shown that, if G is a plane triangulation, then the only zeros of P(G,t) in (−∞...
CPC
2007
14 years 2 months ago
2007
Let P(G,t) and F(G,t) denote the chromatic and flow polynomials of a graph G. G.D. Birkhoff and D.C. Lewis showed that, if G is a plane near triangulation, then the only zeros of...
JCT
2008
14 years 2 months ago
2008
Let M denote the Laplacian matrix of a graph G. Associated with G is a finite group (G), obtained from the Smith normal form of M, and whose order is the number of spanning trees o...
COMBINATORICS
2007
14 years 2 months ago
2007
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) If H is a proper subgraph of a connected graph G o...
COMBINATORICS
2007
14 years 2 months ago
2007
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) Let G be a regular graph of order n and finite di...
ENDM
2006
14 years 2 months ago
2006
Greedy algorithm sometimes uses more than (G) colors while coloring a graph G. A greedy defining set is an object to eliminate these extra colors so that the greedy coloring resul...
DCG
2010
14 years 3 months ago
2010
Consider a graph G with n vertices. In this paper we study geometric conditions for an n-tuple of points in Rd to admit a non-zero self stress with underlying graph G. We introduce...