The square of a block graph

AbstractThe square H2 of a graph H is obtained from H by adding new edges between every two vertices having distance two in H. A block graph is one in which every block is a clique. For the first time, good characterizations and a linear time recognition of squares of block graphs are given in this paper. Our results generalize several previous known results on squares of trees

Distribution-graph based approach and extended tree growing technique in power-constrained block-test scheduling

A distribution-graph based scheduling algorithm is proposed together with an extended tree growing technique to deal with the problem of unequal-length block-test scheduling under power dissipation constraints. The extended tree growing technique is used in combination with the classical scheduling approach in order to improve the test concurrency having assigned power dissipation limits. Its goal is to achieve a balanced test power dissipation by employing a least mean square error function. The least mean square error function is a distribution-graph based global priority function. Test scheduling examples and experiments highlight in the end the efficiency of this approach towards a system-level test scheduling algorithm

Factor Graph Based LMMSE Filtering for Colored Gaussian Processes

We propose a low complexity, graph based linear minimum mean square error (LMMSE) filter in which the non-white characteristics of a random process are taken into account. Our method corresponds to block LMMSE filtering, and has the advantage of complexity linearly increasing with the block length and the ease of incorporating the a priori information of the input signals whenever possible. The proposed method can be used with any random process with a known autocorrelation function with the help of an approximation to an autoregressive (AR) process. We show through extensive simulations that our method performs very close to the optimal block LMMSE filtering for Gaussian input signals.Comment: 5 pages, 4 figure

Tough graphs and hamiltonian circuits

AbstractThe toughness of a graph G is defined as the largest real number t such that deletion of any s points from G results in a graph which is either connected or else has at most s/t components. Clearly, every hamiltonian graph is 1-tough. Conversely, we conjecture that for some t0, every t0-tough graph is hamiltonian. Since a square of a k-connected graph is always k-tough, a proof of this conjecture with t0 = 2 would imply Fleischner's theorem (the square of a block is hamiltonian). We construct an infinite family of (32)-tough nonhamiltonian graphs

Square Sum And Square Difference Labelings Of Semitotal-block Graph For Some Class Of Graphs

A graph G is said to be square sum and square difference labeling, if there exists a bijection f from V (G) to {1, 2, 3, ..., (p − 1)} which induces the injective function f ∗ from E(G) to N, defined by f ∗(uv) = f(u)2 + f(v)2 and f ∗(uv) = f(u)2 − f(v)2 respectively, for each uv ∈ E(G) and the resulting edges are distinctly labeled. G is said to be square sum and square difference graph, if it asdmits a square sum and square difference labeling respectively. The present work investigates, square sum and square difference labelingof semitotal-block graph for some class of graphs which are proved using number theory concept