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- W3185695705 abstract "<abstract><p>Let $ G(V, E) $ be a graph, where $ V(G) $ is the vertex set and $ E(G) $ is the edge set. Let $ k $ be a natural number, a total k-labeling $ varphi:V(G)bigcup E(G)rightarrow {0, 1, 2, 3, ..., k} $ is called an edge irregular reflexive $ k $-labeling if the vertices of $ G $ are labeled with the set of even numbers from $ {0, 1, 2, 3, ..., k} $ and the edges of $ G $ are labeled with numbers from $ {1, 2, 3, ..., k} $ in such a way for every two different edges $ xy $ and $ x^{'}y^{'} $ their weights $ varphi(x)+varphi(xy)+varphi(y) $ and $ varphi(x^{'})+varphi(x^{'}y^{'})+varphi(y^{'}) $ are distinct. The reflexive edge strength of $ G $, $ res(G) $, is defined as the minimum $ k $ for which $ G $ has an edge irregular reflexive $ k $-labeling. In this paper, we determine the exact value of the reflexive edge strength for the $ r $-th power of the path $ P_{n} $, where $ rgeq2 $, $ ngeq r+4 $.</p></abstract>" @default.
- W3185695705 created "2021-08-02" @default.
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- W3185695705 date "2021-01-01" @default.
- W3185695705 modified "2023-09-24" @default.
- W3185695705 title "Edge irregular reflexive labeling for the $ r $-th power of the path" @default.
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- W3185695705 doi "https://doi.org/10.3934/math.2021604" @default.
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