The problem of quantifying the vulnerability of graphs has received much attention nowadays, especially in the field of computer or communication networks. In a communication network, the vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a graph as modeling a network, the average lower 2-d...

We say that a spanning eulerian subgraph F ⊂ G is a flower in a graph G if there is a vertex u ∈ V (G) (called the center of F ) such that all vertices of G except u are of the degree exactly 2 in F. A graph G has the flower property if every vertex of G is a center of a flower. Kaneko conjectured that G has the flower property if and only if G is hamiltonian. In the present paper we prove this...

A flower graph consists of a half line and N symmetric loops connected at single vertex with N≥2 (it is called the tadpole if N=1). We consider positive single-lobe states on in framework cubic nonlinear Schrödinger equation. The main novelty our paper rigorous application period function for second-order differential equations towards understanding symmetries bifurcations standing waves metric...

For any non-trivial abelian group A under addition a graph $G$ is said to be $A$-textit{magic}  if there exists a labeling $f:E(G) rightarrow A-{0}$ such that, the vertex labeling $f^+$  defined as $f^+(v) = sum f(uv)$ taken over all edges $uv$ incident at $v$ is a constant. An $A$-textit{magic} graph $G$ is said to be $Z_k$-magic graph if the group $A$ is $Z_k$  the group of integers modulo $k...

A flower is a coin graph representation of the wheel graph. A petal of a flower is an outer coin connected to the center coin. The results of this paper are twofold. First we derive a parametrization of all the rational (and hence integer) radii coins of the 3-petal flower, also known as Apollonian circles or Soddy circles. Secondly we consider a general n-petal flower and show there is a uniqu...

The present study was undertaken to study the sunscreen activity of herbal formulation. There is no evidence of the sun protection factor (SPF) studies on essential oil of Calendula flowers (Calendula officinalis L., Asteraceae). The study investigates the in vitro SPF by ultraviolet specrtophotometry method of Calendula flower oil in a cream formulation. Calendula oil was isolated by Clavenger...

The sun is the graph obtained from a cycle of length even and at least six by adding edges to make the even-indexed vertices pairwise adjacent. Suns play an important role in the study of strongly chordal graphs. A graph is chordal if it does not contain an induced cycle of length at least four. A graph is strongly chordal if it is chordal and every even cycle has a chord joining vertices whose...