Geodesic
Two graphs with a common edge
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 497-507 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

Let G = G_1 ∪ G_2 be the sum of two simple graphs G_1,G_2 having a common edge or G = G_1 ∪ e_1 ∪ e_2 ∪ G_2 be the sum of two simple disjoint graphs G_1,G_2 connected by two edges e_1 and e_2 which form a cycle C_4 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 G_1 and G_2. To show the scope and effectiveness of our method we give some examples.
Keywords: graph, adjacency matrix, determinant of graph, path, cycle 
@article{DMGT_2014_34_3_a2,
     author = {Badura, Lidia},
     title = {Two graphs with a common edge},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {497--507},
     year = {2014},
     volume = {34},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a2/}
}
TY  - JOUR
AU  - Badura, Lidia
TI  - Two graphs with a common edge
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2014
SP  - 497
EP  - 507
VL  - 34
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a2/
LA  - en
ID  - DMGT_2014_34_3_a2
ER  - 
%0 Journal Article
%A Badura, Lidia
%T Two graphs with a common edge
%J Discussiones Mathematicae. Graph Theory
%D 2014
%P 497-507
%V 34
%N 3
%U http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a2/
%G en
%F DMGT_2014_34_3_a2
Badura, Lidia. Two graphs with a common edge. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 497-507. http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a2/

[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

[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

[5] P. Wojtylak and S. Arworn, Paths of cycles and cycles of cycles, (2010) preprint.