Graph Equations Involving Tensor Product of Graphs
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we solve the following four graph equations $\lkg = H \oplus J ; \mg = H \oplus J ; \overline{\lkg} = H \oplus J $ and $\ov{\mg} = H \oplus J$, where $J$ is $nK_2$ for $n \geq 1$. Here, the equality symbol~ =~ means the isomorphism between the corresponding graphs. In particular, we shall obtain all pairs of graphs $(G,H)$, which satisfy the above mentioned equations, upto isomorphism.
Abstract
In this paper, we solve the following four graph equations $\lkg = H \oplus J ; \mg = H \oplus J ; \overline{\lkg} = H \oplus J $ and $\ov{\mg} = H \oplus J$, where $J$ is $nK_2$ for $n \geq 1$. Here, the equality symbol~ =~ means the isomorphism between the corresponding graphs. In particular, we shall obtain all pairs of graphs $(G,H)$, which satisfy the above mentioned equations, upto isomorphism.
참고문헌 (11)
- M. Behzad, "Introduction to the theory of graphs" (1972), Allyn and Bacon. Inc
- D. M. Cvetkovic, "Spectrum of the total graph of a graph", Publ. Inst. Math. (Beograd), 16(30), pp.49~52 (1973)
- M. Farzan, "Kronecker products and local joins of graphs", Canad. J. Math., 29(2), pp.255~269 (1977)
- T. Hamada, "Traversability and connectivity of the middle graph of a graph", Discrete Math., 14, pp.247~255 (1976)
- F. Harary, "Graph theory" (1969), Addison-Wesley Publishing Co.
- V. R. Kulli, "Graph equations for line graphs, middle graphs and entire graphs", J. Karnatak Univ. Sci., 23, pp.25~28 (1978)
- H. P. Patil, "Characterizations of k-ctrees and graph valued functions", J. Combin. Math. Combin. Comput., 84, pp.91~98 (2013)
- H. P. Patil, "On tensor product of graphs, girth and triangles", Iran. J. Math. Sci. Inform., 10(1), pp.139~147 (2015)
- E. Sampathkumar, "Semi-total graphs of a graph I", J. Karnatak Univ. Sci., 18, pp.274~280 (1973)
- D. V. S. S. Sastry, "Graph equations for line graphs, middle graphs and quasitotal graphs", Discrete Math., 48, pp.113~119 (1984)
- P. M. Weichsel, "The Kronecker product of graphs", Proc. Amer. Math. Soc, 13, pp.47~52 (1962)