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SNM-
35 (Participant)
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SNM-
46 (Participant)
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SNM-
64 (Participant)
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SNM-
81 (Participant)
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SNM-
82 (Participant)
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SNM-
38 (Oral)
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On the Ramsey Number for Trees versus FansThe Ramsey number R(G, H) is the smallest number of vertices r such that any graph F with r vertices either contains G or its complement contains H. In this presentation, we consider R(G,H) where G is a tree Tn of order n, and H is a fan F1,m=K1+Pm. Burr (1981) has provided the lower bound of R(Tn, F1,m). When m ≥ 2n-1, we give the better lower bound for R(Tn, F1,m). We also consider the Ramsey number of Tn versus F1,m for certain values of m when Tn is a tree with maximum degree n-5, n-4, or n-3. In particular, we determine R(Tn, F1,8). when Tn is a tree with maximum degree n-4 or n-5. We also proved that for a tree Tn with maximum degree n-3, the upper bound of R(Tn, F1,m) is R(Sn(1,1),F1,m). Moreover, let x be a vertex with the maximum degree in Tn, and let Tn' be a tree that is constructed from Tn by deleting a pendant edge xu of Tn then connecting u to a pendant vertex of Tn. We show that R(Tn',F1,m) ≤ R(Tn, F1,m) for certain classes of Tn and Tn'. |
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SNM-
45 (Oral)
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The Dominating Partition Dimension of Burger GraphsDominating Partition Dimension is a parameter in graph theory that combines two important concepts: resolving partition and dominating set. A partition of the vertex set V(G) is called a dominating resolving partition if it satisfies two conditions: each vertex in the graph has a unique distance representation with respect to the partition, and each vertex has a neighbor in at least one different partition class. The minimum number of partition classes in a dominating resolving partition is called the dominating partition dimension of a graph G, denoted by η_p (G). This study aims to determine the value of η_p (G) for the burger graph. A burger graph is a cubic graph constructed from two cycles with additional connecting edges between the cycles defined by a specific permutation. Using a theoretical analysis approach to the structure of the graph, partitions that fulfill both resolving and domination properties are identified. The results of this study are expected to enrich the investigation of the η_p (G) parameter in cubic graphs and contribute to the development of regular network models in graph theory. |
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SNM-
108 (Participant)
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SNM-
()
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SNM-
39 (Oral)
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Conceptual metaphor of isomorphisms as bijective homomorphismsHomomorphism and isomorphism groups are essential topics in abstract algebra courses, but studies that demand an understanding of the relationship between these two concepts are still limited. By examining 57 undergraduate student responses (homomorphism assignments), this study explores how conceptual metaphors come into question when faced with problems involving isomorphisms. Starting from how the view that “isomorphism is a bijective homomorphism” can help or complicate students when constructing proofs for isomorphism problems, this study then examines the underlying rationale behind such a perspective. The findings highlight the importance of knowing whether a mapping can be considered a homomorphism or not (utilizing intuition) based on formal definitions and corresponding properties, followed by the conceptual benefit of linking isomorphism and homomorphism into a conceptual metaphor (sameness) as the basis for extending understanding. The implications of understanding homomorphism and isomorphism encourage dialogue on the view of an isomorphism as a bijective homomorphism (an injective and surjective homomorphism), as well as the need to examine further the knowledge content involved. |
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