The Gallai graph and the anti-Gallai graph of a graph G are edge disjoint spanning subgraphs of the line graph L(G). The vertices in the Gallai graph are adjacent if two of the end vertices of the corresponding edges in G coincide and the other two end vertices are nonadjacent in G. The anti-Gallai graph of G is the complement of its Gallai graph in L(G). Attributed to Gallai (1967), the study ...

‎in this paper‎, ‎we define the common minimal dominating signed‎ ‎graph of a given signed graph and offer a structural‎ ‎characterization of common minimal dominating signed graphs‎. ‎in‎ ‎the sequel‎, ‎we also obtained switching equivalence‎ ‎characterizations‎: ‎$overline{s} sim cmd(s)$ and $cmd(s) sim‎ ‎n(s)$‎, ‎where $overline{s}$‎, ‎$cmd(s)$ and $n(s)$ are complementary‎ ‎signed gra...

let $p$ be a prime number and $n$ be a positive integer. the graph $g_p(n)$ is a graph with vertex set $[n]={1,2,ldots ,n}$, in which there is an arc from $u$ to $v$ if and only if $uneq v$ and $pnmid u+v$. in this paper it is shown that $g_p(n)$ is a perfect graph. in addition, an explicit formula for the chromatic number of such graph is given.

hirchsprung’s disease is a developmental disorder of the enteric nervous system, characterized by abdsence of ganglion cell in the myenterric and submucosal plexuese along a variable portion of the distal intestine.the purpose of this study is the presentation of a new procedure for reduction of the postoperative complications of hirschsprung’s disease (hd) by offering a modified swenson’s tech...

background: visceral leishmaniasis is systematic serous parasitic disease with pub­lic health importance. zoonotic form of visceral leishmaniasis is wide spread in mediterranean basin and south america regions. direct agglutination test (dat) is an accurate, reliable and non-expensive serological test for the diagnosis of visceral leishmaniasis in human and canines but the antigen preparation i...

chromium (vi) adsorption behavior and capacity by surface modified nanozeolite a has been investigated. surface modification was performed and the morphology of modified and unmodified nanozeolite was studied using scanning electron microscope (sem) and transmission electron microscope (tem). adsorption isotherms were studied under different conditions (ph, adsorbent dose, adsorbate concentrati...

this paper provides an overview of how the surface properties of ferromagnetic nanoparticles dispersed in fluids is modified by natural and biocompatible polymers. among common magnetic nanoparticles, magnetite (fe3o4) and maghemite (g-fe203) are popular candidates because of their biocompatibility. natural polymeric coating materials are the most commonly used biocompatible magnetic nanopartic...

The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...

Link prediction is a crucial problem in the analysis of graph-structured data, and graph neural networks (GNNs) have proven to be effective addressing this problem. However, computational temporal costs associated with large-scale graphs remain concern. This study introduces novel method for link called Sparse Subgraph Prediction Based on Adaptive Attention (SSP-AA). The generates sparse subgra...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...