Tiraje TUNCER,1 Erdal GİLGİL,2 Cahit KAÇAR,1 Yeşim KURTAİŞ,3 Şehim KUTLAY,3 Bülent BÜTÜN,1 Peyman YALÇIN,3 Ülkü AKARIRMAK,4 Lale ALTAN,5 Füsun ARDIÇ,6 Özge ARDIÇOĞLU,7 Zuhal ALTAY,8 Ferhan CANTÜRK,9 Lale CERRAHOĞLU,10 Remzi ÇEVİK,11 Hüseyin DEMİR,12 Berrin DURMAZ,13 Nigar DURSUN,14 Tuncay DURUÖZ,15 Canan ERDOĞAN,16 Deniz EVCİK,17 Savaş GÜRSOY,18 Sami HİZMETLİ,19 Ece KAPTANOĞLU,19 Önder KAYHAN,1...

‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...

the order graph of a group $g$, denoted by $gamma^*(g)$, is a graph whose vertices are subgroups of $g$ and two distinct vertices $h$ and $k$ are adjacent if and only if $|h|big{|}|k|$ or $|k|big{|}|h|$. in this paper, we study the connectivity and diameter of this  graph. also we give a relation between the order graph and prime  graph of a group.

let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...

in this paper, we first collect the earlier results about some graph operations and then wepresent applications of these results in working with chemical graphs.

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the annihilating-ideal graph of a commutative ring $r$ is denoted by $ag(r)$, whose vertices are all nonzero ideals of $r$ with nonzero annihilators and two distinct vertices $i$ and $j$ are adjacent if and only if $ij=0$. in this article, we completely characterize rings $r$ when $gr(ag(r))neq 3$.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

it is necessary to generate the automorphism group of a chemical graph in computer-aidedstructure elucidation. an euclidean graph associated with a molecule is defined by a weightedgraph with adjacency matrix m = [dij], where for i≠j, dij is the euclidean distance between thenuclei i and j. in this matrix dii can be taken as zero if all the nuclei are equivalent. otherwise,one may introduce dif...

in this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. also, density and balanced irregular vague graphs are discussed and some of their properties are established. finally we give an application of vague digraphs.