let g(v,e) be a graph with p vertices and q edges. a graph g is said to have an odd mean labeling if there exists a function f : v (g) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : e(g) → {1, 3, 5,...,2q - 1} defi ned by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. a graph that admits an odd mean lab...

a 1993 result of j. llibre, and m. misiurewicz, (theorem a [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. also a 1980 result of l.s. block, j. guckenheimer, m. misiurewicz and l.s. young (lemma 1.5 [3]) states that if g is an a-graph of f then h(g) ? h( f ). in this pap...

$!!!!$ in this paper, the notion of fuzzy $!$ krasner $!(m, n)$-hyperrings($!f^{(m, n)}!$-hyperrings) by using the notion of$f^m$-hyperoperations and $f^n$-operations is introduced and somerelated properties are investigated. in this regards,relationships between krasner $f^{(m, n)}$-hyperrings and krasner$(m, n)$-hyperrings are considered. we shall prove that everykrasner $f^{(m, n)}$-hyperrin...

the genera fusicladium, pollaccia and spilocaea are anamorphs of venturia that after conservation of fusicladium against spilocaea, pollaccia, cycloconium and pseudocladosporium, it has been used instead of all anamorph names. during 2011 twigs, leaves and fruits of symptomatic hosts containing fusicladium species from guilan, mazandaran, qazvin and ardabil provinces were sampled and examined. ...

A set C of vertices in a graph G = (V,E) is total dominating in G if all vertices of V are adjacent to a vertex of C. Furthermore, if a total dominating set C in G has the additional property that for any distinct vertices u, v ∈ V \ C the subsets formed by the vertices of C respectively adjacent to u and v are different, then we say that C is a locating-total dominating set in G. Previously, l...