A near-polygonal graph is a graph Γ which has a set C of m-cycles for some positive integer m such that each 2-path of Γ is contained in exactly one cycle in C. If m is the girth of Γ , then the graph is called polygonal. We provide a construction of an infinite family of polygonal graphs of arbitrary even girth with 2-arc transitive automorphism groups, showing that there are infinitely many 2...

LDPC codes are serious contenders to Turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m ≥ 2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m, q) on 2qm vertices, which has girth at least 2dm/2e+ 4. We regard these graphs as Tanner graphs of binar...

A novel method guaranteeing nondecreasing girth is presented for constructing longer low-density parity-check (LDPC) codes from shorter ones. The parity-check matrix of a shorter base code is decomposed into N (N ≥ 2) nonoverlapping components with the same size. Then, these components are combined together to form the parity-check matrix of a longer code, according to a given N×N Latin square....

Partial cubes are graphs isometrically embeddable into hypercubes. We analyze how isometric cycles in partial cubes behave and derive that every partial cube of girth more than six must have vertices of degree less than three. As a direct corollary we get that every regular partial cube of girth more than six is an even cycle. Along the way we prove that every partial cube G with girth more tha...

Partial cubes are graphs isometrically embeddable into hypercubes. We analyze how isometric cycles in partial cubes behave and derive that every partial cube of girth more than six must have vertices of degree less than three. As a direct corollary we get that every regular partial cube of girth more than six is an even cycle. Along the way we prove that every partial cube G with girth more tha...

We describe a sufficient condition for graphs used in a construction of Thomassen (which yields hypohamiltonian graphs) to produce maximally non-hamiltonian (MNH) graphs as well. Then we show that the Coxeter graph fulfils this sufficient condition, and thus applying the Thomassen’s construction to multiple copies of the Coxeter graph yields infinitely many MNH graphs with girth 7. So far, the ...

let $r$ be a commutative ring with identity and $m$ an $r$-module. in this paper, we associate a graph to $m$, say ${gamma}({}_{r}m)$, such that when $m=r$, ${gamma}({}_{r}m)$ coincide with the zero-divisor graph of $r$. many well-known results by d.f. anderson and p.s. livingston have been generalized for ${gamma}({}_{r}m)$. we show that ${gamma}({}_{r}m)$ is connected with ${diam}({gamma}({}_...

‎s‎. ‎kim et al‎. ‎have been analyzed the girth of some algebraically‎ ‎structured quasi-cyclic (qc) low-density parity-check (ldpc)‎ ‎codes‎, ‎i.e‎. ‎tanner $(3,5)$ of length $5p$‎, ‎where $p$ is a prime of‎ ‎the form $15m+1$‎. ‎in this paper‎, ‎by extension this method to‎ ‎tanner $(3,7)$ codes of length $7p$‎, ‎where $p$ is a prime of the‎ ‎form $21m‎+ ‎1$‎, ‎the girth values of tanner $(3,7...

One hundred and ninety two records were taken weekly for twenty four (24) weeks from West African Dwarf (WD), the Yankasa (YN) X crossbred (XB) sheep. The traits evaluated milk yield (MK), linear body measurements (LB) such as height at withers, (HT), length (BL), heart girth (HG), shoulder width (SW), Tail (TA), Neck (NL), circumference (NC), Face (FA), Hind leg (HL), Foreleg (FL), Ear (EA), H...

We consider the complexity of oriented homomorphism and two of its variants, namely strong oriented homomorphism and pushable homomorphism, for planar graphs with large girth. In each case, we consider the smallest target graph such that the corresponding homomorphism is NP-complete. These target graphs T4, T5, and T6 have 4, 5, and 6 vertices, respectively. For i ∈ {4, 5, 6} and for every g, w...