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52 (Participant)
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SNM-
53 (Oral)
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Ascending subgraph decomposition of edge amalgamation of triangles and its antimagic labelingLet t and q be positive integers, and G be a simple and finite graph of size q that satisfy \binom{t+1}{2}≤ q<\binom{t+2}{2}. A graph G admits an ascending subgraph decomposition (ASD) if G can be decomposed into t subgraphs H_1, H_2, … , H_t none of which contain isolated vertices. Moreover, each H_i is isomorphic to a proper subgraph of H_(I+1), for 1≤ i≤ t-1. A conjecture that a graph of positive size has an ASD remains open. In this talk, we present the ascending subgraph decomposition of an edge-amalgamation of triangles. Let f:V(G)∪ E(G)→ {1,2,…,|V(G)|+|E(G)|} be a total labeling on G. If the weights of all H_is (1≤ i≤ t) are distinct, then f is called an ASD-antimagic labeling and G is an ASD-antimagic graph. A further conjecture states that every positive-size graph is ASD-antimagic. In this talk, we support the conjecture by presenting ASD-antimagic labelings for an edge-amalgamation of triangles. The construction of the ASD-antimagic labelings of this graph is based on its H-magic labelings. |
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54 (Participant)
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56 (Participant)
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59 (Participant)
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62 (Participant)
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