# Two Algorithms for Computing All Spanning Trees of a Simple, Undirected, and Connected Graph: Once Assuming a Complete Graph

TL;DR: This paper proposes altogether different and new approaches for the computation of all possible spanning trees of a simple, undirected, and connected graph and proposes to have novelties and limitations of its own.

Abstract: In this paper, we have proposed altogether different and new approaches for the computation of all possible spanning trees of a simple, undirected, and connected graph. Our proposed algorithms have the capability to solve the major bottlenecks in this area, namely, generation of duplicate trees and circuit checking. In the first algorithm, the given graph has been converted to its corresponding weighted complete graph, which proposes to have novelties and limitations of its own. In addition, we have also proposed another related algorithm, and as a result, we have been able to come up with new ideas in this research domain of graph theory.

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756 citations

### "Two Algorithms for Computing All Sp..." refers background in this paper

...Sir Arthur Cayley proposed a formula which states, if Tn is the number of trees of a complete graph of n vertices, then Tn = nn−2 [22]–[24]....

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176 citations

### "Two Algorithms for Computing All Sp..." refers methods in this paper

...[3] H. N. Gabow and E. W. Myers, ‘‘Finding all spanning trees of directed and undirected graphs,’’ SIAM J. Comput., vol. 7, no. 3, pp. 280–287, 1978....

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...Some of the well-known algorithms falling under this category are those proposed by authors like Berger [1], Char [2], Gabow and Myers [3], McIlroy [4], Naskar et al....

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...Some of the well-known algorithms falling under this category are those proposed by authors like Berger [1], Char [2], Gabow and Myers [3], McIlroy [4], Naskar et al. [5]–[7], 56290 2169-3536 2018 IEEE....

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116 citations

### "Two Algorithms for Computing All Sp..." refers methods in this paper

...[13] S. Kapoor and H. Ramesh, ‘‘Algorithms for enumerating all spanning trees of undirected and weighted graphs,’’ SIAM J. Comput., vol. 24, no. 2, pp. 247–265, 1995....

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...Some algorithms following this method of tree generation are those of Cherkasskii [11], Hakimi [12], Kapoor and Ramesh [13], Matsui [14], [15], Mayeda and Seshu [16], Shioura and Tamura [17], Shioura et al. [18], and many others. iii....

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...Some algorithms following this method of tree generation are those of Cherkasskii [11], Hakimi [12], Kapoor and Ramesh [13], Matsui [14], [15], Mayeda and Seshu [16], Shioura and Tamura [17], Shioura et al....

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103 citations

### "Two Algorithms for Computing All Sp..." refers methods in this paper

...These three techniques are tree testing [1]–[10] elementary tree transformation [11]–[18], and successive reduction [19]–[21] methods....

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