Banyak Pohon Pembangun pada Graf Barbell

Maulana, Muklas; Switrayni, Ni Wayan

doi:10.29303/emj.v1i2.46

Cited by 1 publication

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“…In graph theory, there is a topic called the number of spanning trees on a graph. In [18], a tree is defined as a connected graph that has no cycle. The number of spanning trees of a connected graph is defined as the number of trees that can be constructed from the graph which passes through all of its vertices.…”

Section: Introductionmentioning

confidence: 99%

“…In [4], the authors obtained some formulas about the number of spanning trees of the fan graph, complete graph, and wheel graph. Then in 2019, Maulana and Switrayni [18] obtained some formulas about the number of spanning trees of the barbell graph. In this article, we will give some characteristics of the prime graph of the integer modulo group.…”

Section: Introductionmentioning

confidence: 99%

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Some Characteristics of the Prime Graph of Integer Modulo Groups

Maulana

Wardhana

Switrayni

et al. 2023

InPrime:Ind.Jour.Pure.Applied.Math

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The notion of the prime graph of a ring R was first introduced by Bhavanari, Kuncham, and Dasari in 2010. The prime graph of a ring R, denoted by PG(R) is a graph whose vertices are all elements of the ring, where two distinct vertices x and y are adjacent if and only if xRy = 0 or yRx = 0. In this paper, we study the forms and properties of the prime graph of integer modulo group, and some examples of the number of its spanning trees. In this paper, it is found that for all n, the maximum degree of vertices of PG(Z_n) is n-1 and the minimum degree of its vertices is 1. Then, we show that for all n, PG(Z_n) is neither a Hamiltonian graph nor an Eulerian graph. We also found some examples of the number of its spanning trees.Keywords: prime graph; spanning trees; Hamiltonian graph. AbstrakKonsep mengenai graf prima dari suatu gelanggang R pertama kali diperkenalkan oleh Bhavanari, Kuncham, dan Dasari pada tahun 2010. Graf prima dari suatu gelanggang R, yang dinotasikan dengan PG(R), adalah suatu graf yang simpul-simpulnya merupakan semua elemen dari gelanggang tersebut dengan dua buah simpul x dan y yang berbeda akan bertetangga jika dan hanya jika xRy = 0 atau yRx = 0. Di dalam penelitian ini, dikaji mengenai bentuk-bentuk dan sifat-sifat dari PG(Z_n), dan beberapa contoh dari banyak pohon pembangunnya. Pada penelitian ini, ditemukan hasil bahwa untuk setiap n, derajat maksimal dari simpul-simpul di PG(Z_n) adalah n-1 dan derajat minimum dari simpul-simpulnya adalah 1. Hasil selanjutnya yaitu, untuk setiap n, PG(Z_n) bukan merupakan suatu graf Hamiltonian atau graf Eulerian. Ditemukan juga beberapa contoh dari banyaknya pohon pembangun dari PG(Z_n).Kata Kunci: graf prima; pohon pembangun; graf Hamiltonian. 2020MSC: 05E16, 05C90, 20C05

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%