DISCLAIMER: Everything that follows is of a preliminary nature. We give a new invariant for finitely generated groups, called the girth. Several results which indicate that the girth of a group might possibly be a quasi-isometry invariant are proved. We also compute the girth in several instances and speculate on the relation of girth to the growth of groups.

a set $wsubseteq v(g)$ is called a resolving set for $g$, if for each two distinct vertices $u,vin v(g)$ there exists $win w$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. the minimum cardinality of a resolving set for $g$ is called the metric dimension of $g$, and denoted by $dim(g)$. in this paper, it is proved that in a connected graph $...

The objective of this study was to determine the relationship between body weight (BW) and heart girth (HG) in Sardi and Timahdite sheep in order to develop a prediction equation of BW from HG. The data used for this study included 476 records on BW and HG (227 in Sardi and 249 in Timahdite) collected on males and females of different ages in 33 private farms. The BW and the HG averaged 34.8 ± ...

For an arbitrary (3,L) QC-LDPC code with a girth of twelve, a tight lower bound of the consecutive lengths is proposed. For an arbitrary length above the bound the resultant code necessarily has a girth of twelve, and for the length meeting the bound, the corresponding code inevitably has a girth smaller than twelve. The conclusion can play an important role in the proofs of the existence of la...

Phenotypic characterization and body biometric in 13 traits (height at withers, body length, chest girth, paunch girth, ear length, tail length, length of tail up to switch, face length, face width, horn length, circumference of horn at base, distances between pin bone and hip bone) were recorded in 233 adult Gojri buffaloes from Punjab and Himachal Pradesh states of India. Traits were analysed...

Graph G is the square of graph 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 . Given H it is easy to compute its square H, however Motwani and Sudan proved that it is NP-complete to determine if a given graph G is the square of some graph H (of girth 3). In this paper we consider the characterization and recognition problems of graphs that are squ...

My research revolves around structural and extremal aspects of Graph Theory, particularly problems involving girth and distance, trees, cycles in graphs, and some variations of Ramsey theory. I have also done some work in generalized graph colorings and graph labellings. My other interests include graph decomposi-tions and packings, perfect graphs, matching theory, hypergraphs and coding theory...

All weakly distance-regular digraphs with girth $2$ and k-k_{1,1}=1 are classified. A Family of Weakly Distance-Regular Digraphs of Girth 2 Kaishun Wang∗ School of Mathematical Sciences Beijing Normal University Beijing 100875, P.R. China Abstract All weakly distance-regular digraphs with girth 2 and k − k1,1 = 1 are classified.All weakly distance-regular digraphs with girth 2 and k − k1,1 = 1 ...

BACKGROUND Determination of serum uric acid concentrations and role in risk of metabolic syndrome (MS) were investigated in 1877 participants in a cross-sectional population-based study including a brief follow-up. METHODS The MS was identified by modified criteria of the Adult Treatment Panel III, and coronary heart disease (CHD) by clinical findings and Minnesota coding of resting electroca...