Isogeny volcanoes are an interesting structure that have had several recent applications. An isogeny volcano is a connected component of a larger graph called a cordillera. In this paper, we further explore properties of how to compute volcanoes given that we have already computed one of a different degree. This allows us to compute volcanoes of composite degree more efficiently than a direct c...

SUMMARY Network motifs in integrated molecular networks represent functional relationships between distinct data types. They aggregate to form dense topological structures corresponding to functional modules which cannot be detected by traditional graph clustering algorithms. We developed CyClus3D, a Cytoscape plugin for clustering composite three-node network motifs using a 3D spectral cluster...

let $g$ be a non-abelian finite group. in this paper, we prove that $gamma(g)$ is $k_4$-free if and only if $g cong a times p$, where $a$ is an abelian group, $p$ is a $2$-group and $g/z(g) cong mathbb{ z}_2 times mathbb{z}_2$. also, we show that $gamma(g)$ is $k_{1,3}$-free if and only if $g cong {mathbb{s}}_3,~d_8$ or $q_8$.

we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

node naming function, 121abstract window toolkit, see AWTacyclic graph, 29API, 260application initializer plug-in, 305application library, 284application programming interface, see APIassociation class, 202, 236association classifier, 14, 205automatic documentation, 27AWT, 303 BDP, 156bend, 54, 137, 233bipartite crossing numbers, 163bipartite ...

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

With the ever-increasing diversification of people's interests and preferences, artwork has become one most popular commodities or investment goods in E-commerce, it increasingly attracts attention public. Currently, many real-world virtual artworks can be found finding a means to recommend them appropriate users significant task alleviate heavy burden on selection decisions by users. Existing ...