Another Antimagic Decomposition of Generalized Peterzen Graph
Abstract
Abstract
A decomposition of a graph P into a family Q consisting of isomorphic copies of a graph Q is (a,b)-Q-antimagic if there is a bijection φ:V(P)∪E(P)→{1,2,3,4…,v_P+e_P} such that for all subgraphs Q’ isomorphic to Q, the Q-weights
φ(Q’ )=∑_(v∈V(Q^' ))▒φ(v) + ∑_(e∈E(Q^'))▒〖φ(e)〗
constitute an arithmetic progression a,a + b,a + 2b,…,a + (r - 1)b where a and b are positive integers and r is the number of subgraphs of P isomorphic to Q. In this article, we prove the existence of a (a,b)-P_4-antimagic decomposition of a generalized Peterzen graph GPz(n,3) for several values of b.
Keywords: covering; decomposition; antimagic; generalized Peterzen.
Abstrak
Suatu dekomposisi dari suatu graf P ke dalam suatu famili Q yang terdiri dari salinan isomorfik dari graf Q dikatakan (a,b)-Q-antiajaib jika terdapat pemetaaan bijektif φ:V(P)∪E(P)→{1,2,3,4…,v_P+e_P} sedemikian sehingga semua subgraf Q’ yang isomorfik ke Q, dengan bobot-Q sebagai berikut
φ(Q’ )=∑_(v∈V(Q^' ))▒φ(v) + ∑_(e∈E(Q^'))▒〖φ(e)〗
yang membentuk suatu barisan aritmatika yaitu a,a + b,a + 2b,…,a + (r - 1)b dengan a dan b adalah bilangan bulat positif dan r adalah banyaknya subgraf dari P yang isomorfik ke Q. Pada artikel ini, kami membuktikan eksistensi (a,b)-P_4-antiajaib dekomposisi dari graf generalized Peterzen GPz(n,3) untuk beberapa nilai b.
Kata kunci: selimut; dekomposisi; antiajaib; generalized Peterzen.
Keywords
References
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DOI: 10.15408/inprime.v3i2.19954
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