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37 (Oral)
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On Ramsey (2K_2,S_n)-Minimal Graphs of the Smallest OrderThe notation F → (G,H) means that for every red-blue edge coloring of F, the red subgraph contains a copy of G or the blue subgraph contains a copy of H. Let ℛ(G,H) denote the set of all graphs F such that F → (G,H), and for every edge e ∈ E(F), it holds that F − e ↛ (G,H). The minimum order of graphs in ℛ(G,H) is denoted by R ̂(G,H). A star graph Sₙ is defined as the join of K₁ and (K_n ) ̅, where K̅ₙ is the edgeless graph on n vertices. In this talk, we determine all graphs in R ̂(2K₂, Sₙ) for every n ≥ 3. |
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36 (Participant)
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66 (Participant)
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SNM-
10 (Oral)
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Outer Multiset Dimension of Products with Complete and Null GraphsThe outer multiset dimension of graph G, dimms(G), is the cardinality of the smallest subset S of vertices that uniquely recognizes each vertex outside S by using the multiset of distances between the vertex and the vertices in S. This paper considers the outer multiset dimensions of graphs obtained for three products (lexicographic, corona, and extended corona) with complete or null graphs. We provide sharp lower bounds for such product graphs. We construct graphs whose outer multiset dimension is close to the lower bound. Further, in the case of lexicographic and corona product graphs, we characterize graphs whose outer multiset dimension is the lower bound |