Abstract
Realization of graphic sequences and finding the spanning tree of a graph are two popular problems of combinatorial optimization. A simple graph that realizes a given non-negative integer sequence is often termed as a realization of the given sequence. In this paper we have proposed a method for obtaining a spanning tree directly from a degree sequence by applying BFS and DFS algorithm separately, provided the degree sequence is graphic and non-regular. The proposed method is a two step process. First we apply an algorithm to check whether the input sequence is realizable through the construction of the adjacency matrix corresponding to the degree sequence. Then we apply the BFS and DFS algorithm separately to generate the spanning tree from it.
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References
Havel, V.: A remark on the existence of finite graphs. (Czech.) Casopis Pest. Mat. 80, 477–480 (1955)
Hakimi, S.L.: On the realizability of a set of integers as degrees of the vertices of a graph. SIAM J. Appl. Math. 10, 496–506 (1962)
Erdὅs, P., Gallai, T.: Graphs with prescribed degree of vertices. (Hungarian) Mat. Lapok. 11, 264–274 (1960)
Ryser, H.J.: Combinatorial properties of matrices of zeros and ones. Can. J. Math. 9, 371–377 (1957)
Berge, C.: Graphs and Hypergraphs. Elsevier, New York (1973)
Fulkerson, D.R., Hofman, A.J., McAndrew, M.H.: Some properties of graphs with multiple edges. Can. J. Math. 17, 166–177 (1965)
Bollobảs, B.: Extremal Graph Theory. Acedemic Press, New York (1978)
Grá½”nbaum, B.: Graphs and complexes. Report of the University of Washington, Seattle, Math. 572B (1969) (private communication)
Hässelbarth, W.: Die Verzweighteit von Graphen. Match. 16, 3–17 (1984)
Sierksma, G., Hoogeveen, H.: Seven criteria for integer sequences being graphic. J. Graph Theory 15(2), 223–231 (1991)
Tripathi, A., Vijay, S.: A note on theorem on Erdὅs and Gallai. Discret Math. 265, 417–420 (2003)
Dahl, G., Flatberg, T.: A remark concerning graphical sequences. Discret. Math. 304, 62–64 (2005)
Tripathi, A., Taygi, H.: A simple criterion on degree sequences of graphs. Discret. Appl. Math. 156, 3513–3517 (2008)
Kleitman, D.J., Wang, D.L.: Algorithms for constructing graphs and digraphs with given valences and factors. Discret. Math. 6, 79–88 (1973)
Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. Elsevier, New York (1976)
Czajkowski, R., Eggleton, B.: Graphic sequences and graphic polynomials: a report. Infin. Finite Sets. 1, 385–392 (1973)
Prim, R.C.: Shortest connection networks and some generalizations. Bell Syst. Technic. J. 4, 53–57 (1957)
Kruskal, J.B.: On the shortest spanning subtree of a graph and the travelling salesman problem. Proc. Am. Math. Soc. 7, 48–50 (1956)
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Biswas, P., Paul, A., Gogoi, A., Bhattacharya, P. (2016). An Efficient Approach for Constructing Spanning Trees by Applying BFS and DFS Algorithm Directly on Non-regular Graphic Sequences. In: Shetty, N., Prasad, N., Nalini, N. (eds) Emerging Research in Computing, Information, Communication and Applications. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2553-9_39
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DOI: https://doi.org/10.1007/978-81-322-2553-9_39
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