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arXiv · 2510.26176

The Morse complex of the wedge of two extended star graphs and a path

Shuma Komatsu
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Abstract

In the work of C. Donovan and N. A. Scoville, the homotopy type of the Morse complex of the extended star graph which is obtained as the one-point union of n paths of length 2 was determined by using star clusters and Cluster Lemma. In this paper, we determine the homotopy type of the Morse complex of extended star graph consisting of a path of length 1 and n paths of length 2 by using strong collapses and Hasse diagram. Furthermore, we compute the homotopy type of the graph obtained by attaching the center vertices of two extended star graphs to different endpoints of a path by using star clusters and the Cluster Lemma.

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Shuma Komatsu. 2025-10-30. The Morse complex of the wedge of two extended star graphs and a path. https://arxiv.org/abs/2510.26176

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