A total $m$-labelling $\alpha$ on graph $\Gamma$ is called an edge irregular total $m$-labelling if for any two different edges of $\Gamma$, their weights respect to $\alpha$ are distinct, where the weight of any edge is defined as the sum of its label and the labels of its end vertices. We determine the minimum $m$ such that $\Gamma$ can be labelled by an edge irregular total $m$-labelling whenever $\Gamma$ is an odd staircase graph or an even staircase graph.
This study examines the significance of the contribution of Islamic Religious Education (PAI) teachers in shaping the noble character of students at MA Zainal Arifin Terate Sumenep. The thesis employs a qualitative approach and a descriptive method. Based on observations, it can be concluded that the formation of students with noble character is one of the visions of MA Zainal Arifin. To achieve this vision, MA Zainal Arifin provides conceptual, practical, comprehensive, and integrated Islamic education with the pesantren system. This policy is supported by all parties, from the Foundation, Head of the Madrasah, Teachers, Society, to the MA Zainal Arifin students themselves. The contribution of PAI in shaping the noble character of MA Zainal Arifin students is significant because of two factors. Firstly, the PAI curriculum at MA Zainal Arifin is comprehensive as it covers all aspects of Islamic Religious Education. Secondly, the education system at MA Zainal Arifin is integrated with the pesantren system.
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