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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2014 | 34 | 3 | 497-507

## Two Graphs with a Common Edge

EN

### Abstrakty

EN
Let G = G1 ∪ G2 be the sum of two simple graphs G1,G2 having a common edge or G = G1 ∪ e1 ∪ e2 ∪ G2 be the sum of two simple disjoint graphs G1,G2 connected by two edges e1 and e2 which form a cycle C4 inside G. We give a method of computing the determinant det A(G) of the adjacency matrix of G by reducing the calculation of the determinant to certain subgraphs of G1 and G2. To show the scope and effectiveness of our method we give some examples

EN

497-507

wydano
2014-08-01
otrzymano
2012-10-30
poprawiono
2013-05-08
zaakceptowano
2013-05-08
online
2014-07-16

### Twórcy

autor
• Mathematics and Computer Science Department University of Opole Oleska 48 45-052 Opole, Poland

### Bibliografia

• [1] A. Abdollahi, Determinants of adjacency matrices of graphs, Trans. Combin. 1(4) (2012) 9-16.
• [2] F. Harary, The Determinant of the adjacency matrix of a graph, SIAM Rev. 4 (1961) 202-210. doi:10.1137/1004057[Crossref]
• [3] L. Huang and W. Yan, On the determinant of the adjacency matrix of a type of plane bipartite graphs, MATCH Commun. Math. Comput. Chem. 68 (2012) 931-938.
• [4] H.M. Rara, Reduction procedures for calculating the determinant of the adjacency matrix of some graphs and the singularity of square planar grids, Discrete Math. 151 (1996) 213-219. doi:10.1016/0012-365X(94)00098-4[Crossref]
• [5] P. Wojtylak and S. Arworn, Paths of cycles and cycles of cycles, (2010) preprint.