A two-colored digraph D (2) is primitive provided there are nonnegative integers h and k such that for each pair of not necessarily distinct vertices u and v in D (2) there exists a (h, k)-walk in D (2) from u to v. The exponent of a primitive twocolored digraph D (2) , exp(D (2)), is the smallest positive integer h + k taken over all such nonnegative integers h and k. The exponent of a vertex v in D (2) is the smallest positive integer s + t such that for each vertex u in D (2) there is an (s, t)-walk from v to u. We study the vertex exponents of primitive two-colored digraphs L (2) n on n ≥ 5 vertices whose underlying digraph is the Hamiltonian digraph consisting of the cycle v 1 → vn → v n−1 → • • • → v 2 → v 1 and the arc v 1 → v n−2. For such two-colored digraph it is known that 2n 2 − 6n + 2 ≤ exp(L (2) n) ≤ (n 3 − 2n 2 + 1)/2. We show that if exp(L (2) n) = (n 3 − 2n 2 + 1)/2, then its vertex exponents lie on [(n 3 − 2n 2 − 3n + 4)/4, (n 3 − 2n 2 + 3n + 6)/4] and if exp(L (2) n) = 2n 2 − 6n + 2, then its vertex exponents lie on [n 2 − 4n + 5, n 2 − 2n − 1].

Laboratories are very important in primary and secondary educational levels. Laboratories with practical activities can help students understand the concepts they have learned in class so as to increase their learning interest in science. One of the competencies in the learning process is the ability of students to solve problems in their life. This can be achieved with the help of laboratories and teaching aids available at the school. The psychomotor abilities of students will be honed in solving problems related to science concepts. Community service activities are carried out by several methods, the initial survey of partner problems, designing teaching aids and practicum equipment, simple practicum in the laboratory and making a practical guidebook. In the lab activities in the laboratory, the pre-test value was obtained with an average of 51.38 with the highest score was 70 and the lowest was 20. While the post-test score had an average of 79.31 with the highest score was 100 and the lowest was 30. The pre-test and post-test results showed an increase in the average value of students by 54.36%.

Laboratorium merupakan sarana yang sangat penting keberadaaannya di satuan pendidikan dasar dan menengah. Laboratorium dengan aktivitas praktikumnya dapat membantu pemahaman siswa terhadap konsep yang dipelajarinya di kelas sehingga meningkatkan minat belajar siswa terhadap sains. Salah satu kompetensi dalam proses belajar mengajar adalah kemampuan siswa memecahkan masalah di kehidupan sehari-hari. Ini bisa tercapai dengan bantuan laboratorium beserta alat peraga yang tersedia di sekolah. Kemampuan psikomotorik siswa akan terasah dalam memecahkan masalah-masalah yang berkaitan dengan konsep sains. Kegiatan pengabdian kepada masyarkat dilakukan dengan beberapa metode yaitu survey awal terhadap permasalahan mitra, merancang alat peraga dan peralatan praktikum, praktikum sederhana di laboratorium danmembuat buku penuntun praktikum. Pada kegiatan praktikumdi laboratorium diperoleh nilai pre-test dengan rata-rata 51,38 dengan nilai tertinggi 70 dan terendah 20. Sedangkan nilai post-test memiliki rata-rata 79,31 dengan nilai tertinggi 100 dan terendah 30. Hasil pre-test dan post-test ini menunjukkan adanya kenaikan nilai rata-rata siswa sebesar 54,36%.

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This paper is about an asymmetric two-coloured cycle. Let D be an asymmetric two-coloured cycle on n vertices, where n is odd and n >= 3, we show that the exponent of the k-th vertex of D is exactly (n2-1)/4 + ⌊ k/2 ⌋.