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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Abstract
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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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