A graph $G$ is called $P_4$-free, if $G$ does not contain an induced subgraph $P_4$. The domination polynomial of a graph $G$ of order $n$ is the polynomial $D(G,x)=sum_{i=1}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$. Every root of $D(G,x)$ is called a domination root of $G$. In this paper we state and prove formula for the domination polynomial of no...

Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...

We present a fully computer-assisted proof system for solving particular family of problems in Extremal Combinatorics. Existing techniques using Flag Algebras have proven powerful the past, but so far lacked computational counterpart to derive matching constructive bounds. demonstrate that common search heuristics are capable finding constructions beyond reach human intuition. Additionally, mos...

The feasible region $\Omega_{{\rm ind}}(F)$ of a graph $F$ is the collection points $(x,y)$ in unit square such that there exists sequence graphs whose edge densities approach $x$ and induced $F$-densities $y$. A complete description not known for any with at least four vertices clique or an independent set. provides lot combinatorial information about $F$. For example, supremum $y$ over all $(...

Pengembangan teknologi di berbagai bidang dari tahun ke semakin pesat, begitu pula pengembangan kedirgantaraan. Salah satu pengembangannya adalah pesawat tanpa awak atau Unmanned Aerial Vehicle (UAV). Dalam penelitian ini, dilakukan analisis sistem dan desain kontrol pada model gerak lateral-direksional UAV menggunakan Output Feedback Control. Sistem bersifat tidak stabil, terkontrol, teramati....

The Turán number of an $r$-uniform graph $F$, denoted by $ex(n,F)$, is the maximum edges in $F$-free on $n$ vertices. density $F$ defined as $\pi(F)=\underset{{n\rightarrow\infty}}{\lim}{ex(n,F) \over {n \choose r }}.$ Denote $\Pi_{\infty}^{(r)}={ \pi(\cal F): \cal F a family r{-uniform graphs}},$ $\Pi_{fin}^{(r)}=\{ {is \ finite of} r{{-}uniform graphs}\}$, and $\Pi_{t}^{(r)}=\{\pi(\cal graphs...

‎In this paper, first we introduce the end of locally finite graphs as an equivalence class of infinite paths in the graph. Then we mention the ends of finitely generated groups using the Cayley graph. It was proved that the number of ends of groups are not depended on the Cayley graph and that the number of ends in the groups is equal to zero, one, two, or infinity. For ...

in this paper, we examine that some simple $k_4$-groups can be determined uniquely by their orders and one or two irreducible complex character degrees.