Finding The Number of Spanning Trees on The Tricyclic Graph
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Abstract
For each and a connected graph
of order
is said to be a
-cyclic graph if
is a graph with size
and a 3-cyclic graph is said to be a tricyclic graph. In this paper, we find the number of spanning trees on the tricyclic graph, considering 4 types from the number of cycles. Then use the counting techniques to find the number of spanning trees on the tricyclic graph of each type.
Keywords: Spanning tree, Number of spanning trees of graph, Tricyclic
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References
นิรุตติ์ พิพรรธนจินดา. (2560). ทฤษฎีกราฟเบื้องต้น. กำแแพงเพชร: มหาวิทยาลัยราชภัฏกำแพงเพชร.
Pipattanajinda, N. (2017). Introduction to graph theory. Kampheng Phet: Kamphaeng Phet Rajabhat University.
ปัฐยา มีสุข และ นิรุตติ์ พิพรรธนจินดา. (2563). สูตรการหาจํานวนต้นไม้แผ่ทั่วของกราฟ
-วัฏจักร. วารสารคณิตศาสตร์ราชภัฏ. 5 (1), น. 23 – 34.
Meesuk, M., and Pipattanajinda, N. (2020). A Formula for Finding The Number of Spanning Trees on The Bicyclic Graph. Rajabhat Mathematics Journal. 5 (1), p. 23 – 34.
Abu-Sbeih, M. Z. (1990). On The Number of Spanning Tree of K_n and K_(n,m). Discrete Mathematics, 84 (2), p. 205 – 207.
Cayley, A. (1889). A Theorem on Trees, Quart. J. Pure Appl. Math. 23, p. 376 – 378.
Kirchhoff, G. (1847). Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird, Annalen der Physik, 148, p. 497 – 508.
Li, J. and Shiu, W. C. (2014). The Number of Spanning Trees of Composite Graphs. J. of Combi. Math. and Combi. Compu. 89, p. 45 – 52.
Li, J., Shiu, W. C. and Chang, A. (2010). The Number of Spanning Trees of
A Graph. Appl. Math. Letters. 23 (3), p. 286 – 290.