Abstract. Let G(V, E) be a graph of vertex set V and edge set E. Local vertex antimagic total coloring developed from local edge and local vertex antimagic coloring of graph. Local vertex antimagic total coloring is defined f
Graph coloring began to be developed into coloring dynamic. One of the developments of dynamic coloring is $r$-dynamic total coloring. Suppose $G=(V(G),E(G))$ is a non-trivial connected graph. Total coloring is defined as $c:(V(G) \cup E(G))\rightarrow {1,2,...,k}, k \in N$, with condition two adjacent vertices and the edge that is adjacent to the vertex must have a different color. $r$-dynamic total coloring defined as the mapping of the function $c$ from the set of vertices and edges $(V(G)\cup E(G))$ such that for every vertex $v \in V(G)$ satisfy $|c(N(v))| = min{[r,d(v)+|N(v)|]}$, and for each edge $e=uv \in E(G)$ satisfy $|c(N(e))| = min{[r,d(u)+d(v)]}$. The minimal $k$ of color is called $r$-dynamic total chromatic number denoted by $\chi^{\prime\prime}(G)$. The $1$-dynamic total chromatic number is denoted by $\chi^{\prime\prime}(G)$, chromatic number $2$-dynamic denoted with $\chi^{\prime\prime}_d(G)$ and $r$-dynamic chromatic number denoted by $\chi^{\prime\prime}_r(G)$. The graph that used in this research are path graph, $shackle$ of book graph $(shack(B_2,v,n)$ and \emph{generalized shackle} of graph \emph{friendship} $gshack({\bf F}_4,e,n)$.
If there exist two vertices on a given graph that are not connected by a path, then we call that graph is disconnected. Given a graph with n vertices and m edges, then a lot of graphs can be constructed. In this paper, we discuss the number of disconnected vertices labeled graphs of order six (n = 6) with the maximum number of parallel edges is twenty. Moreover, a maximum number of edges that connect different pair of vertices is ten (parallel edges are counted as one) and containing no loops (isomorphic graphs are counted as one).
Perguruan Tinggi Negeri (PTN) adalah salah satu jenjang studi tujuan dari siswa SMA setelah lulus. Lembaga yang menjadi penyelenggara tes masuk perguruan tinggi bagi calon mahasiswa baru yaitu Lembaga Tes Masuk Perguruan Tinggi (LTMPT). Berdasarkan data LTMPT Tahun 2021 yang dapat diakses di top-1000-sekolah.ltmpt.ac.id, 5 peringkat peraih nilai Ujian Tulis Berbasis Kompetensi secara nasional tertinggi berasal dari SMA/sederajat dari Jawa. Sedangkan SMA/sederajat di Kota Samarinda menempati peringkat mulai dari 419. Hal ini dikhawatirkan menurunkan daya saing siswa/i Kota Samarinda untuk diterima di perguruan tinggi negeri. Oleh karena itu, dalam pengabdian masyarakat ini akan dilakukan Pelatihan Tes Kemampuan Akademik (TKA) Bidang Matematika untuk siswa kelas 12 SMA Kota Samarinda. Dengan harapan untuk memberikan pengalaman dan pemahaman Tes Kemampuan Akademik kepada Siswa/i kelas 12 Kota Samarinda. Kota Samarinda dipilih karena kemudahan akses dan siswa kelas 12 SMA dipilih karena termasuk peserta didik tingkat akhir. Metode pelatihan yang digunakan adalah tatap muka, ceramah, latihan dan diskusi. Peserta diberikan tes awal sebelum pelatihan dan peserta diberikan tes akhir setelah pelatihan. Data tes awal dan tes akhir dianalisis menggunakan statistika deskriprif dan uji beda rata-rata. Hasilnya terdapat perbedaan rata-rata pada tes awal dan tes akhir, dan rata-rata tes awal < rata-rata tes akhir. Artinya tim pengabdian kepada masyarakat berhasil memberikan pengalaman dan pemahaman kepada peserta pelatihan Tes Kemampuan Akademik di Kota Samarinda.
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