# Two Graphs with a Common Edge

Discussiones Mathematicae Graph Theory (2014)

- Volume: 34, Issue: 3, page 497-507
- ISSN: 2083-5892

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topLidia Badura. "Two Graphs with a Common Edge." Discussiones Mathematicae Graph Theory 34.3 (2014): 497-507. <http://eudml.org/doc/267692>.

@article{LidiaBadura2014,

abstract = {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},

author = {Lidia Badura},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph; adjacency matrix; determinant of graph; path; cycle},

language = {eng},

number = {3},

pages = {497-507},

title = {Two Graphs with a Common Edge},

url = {http://eudml.org/doc/267692},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Lidia Badura

TI - Two Graphs with a Common Edge

JO - Discussiones Mathematicae Graph Theory

PY - 2014

VL - 34

IS - 3

SP - 497

EP - 507

AB - 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

LA - eng

KW - graph; adjacency matrix; determinant of graph; path; cycle

UR - http://eudml.org/doc/267692

ER -

## References

top- [1] A. Abdollahi, Determinants of adjacency matrices of graphs, Trans. Combin. 1(4) (2012) 9-16. Zbl1272.05107
- [2] F. Harary, The Determinant of the adjacency matrix of a graph, SIAM Rev. 4 (1961) 202-210. doi:10.1137/1004057[Crossref] Zbl0113.17406
- [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. Zbl1289.05293
- [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.

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