Square Root Finding In Graphs

Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Graph square is a basic operation with a number of results about its properties in the literature. We study the characterization and recognition problems of graph powers. There are algorithmic and computational approaches to answer the decision problem of whether a given graph is a certain power of any graph. There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four. The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs with girth 5 is NP-complete. This result is providing the complete dichotomy theorem for square root finding problem.

The Falls of Niagara : being a complete guide to all the points of interest around and in the immediate neighbourhood of the great cataract with views taken from sketches by Washington Friend, and from photographs. --

Includes index.

The complete illustrated guide to Niagara Falls and vicinity. -

Attributed to Peter Augustus Porter--National Union Catalog, pre-1956 imprints.

A New guide to Niagara Falls and vicinity : giving a full and complete description of Niagara Falls, suspension bridge, Buffalo, Rochester, Ontario beach, Toronto, Lockport, Tonawanda, Lewiston, Niagara-on-the-Lake, Chautauqua, and other places of interest. --

Cover title: Illustrated guide to Niagara Falls and vicinity.

Complete Genome Sequence of Erwinia amylovora Bacteriophage

The complete genome of an Erwinia amylovora bacteriophage, vB_EamM_Ea35-70 (Ea35-70), is 271,084 bp, encodes 318 putative proteins, and contains one tRNA. Comparative analysis with other Myoviridae genomes suggests that Ea35-70 is related to the Phikzlikevirus genus within the family Myoviridae, since 26% of Ea35-70 proteins share homology to proteins in Pseudomonas phage φKZ.

1493 BH17 NP 2014

Brown sediment with clasts ranging from small to large. Clast shape ranges from angular to rounded. Lineations and comet structures are abundant throughout this sample. It also contains rotation structures and minor amounts of grain crushing.

1501 BH17 NP 2014

Brown sediment with clasts ranging from small to large in size. Clast shape ranges from angular to sub-rounded. Lineations and comet structures are commonly seen throughout the sample. Rotation structures with and without central grains can also be seen.

1507 BH17 NP 2014

Brown sediment with clasts ranging from small to large in size. Clast shape ranges from angular to rounded. Lineations and rotation structures were abundant in this sample, Rotation structures were seen with and without central grains. Comet structures were also present in this sample along with minor amounts of grain stacking.

1520 BH17 NP 2014

Dark brown sediment with clasts ranging from small to large in size. Clast shape ranges from angular to sub-rounded. Lineations can be seen throughout the sample, along with a few rotation and comet structures. This sample also contains a fine grained clay domain that is relatively structure-less. It can be seen scattered throughout the sample.

1523 BH17 NP 2014

Brown sediment with clasts ranging from small to large in size. Clast shape ranges from angular to sub-rounded. Lineations and rotation structures are abundant throughout the sample. Comet structures can also be seen. Minor amounts of grains crushing/stacking are also present.