6533b7ddfe1ef96bd12754da

RESEARCH PRODUCT

Two graphs with a common edge

Lidia Badura

subject

Discrete mathematicsBlock graphadjacency matrixcycleApplied MathematicsSymmetric graphpathComparability graphgraphdeterminant of graphlaw.inventionCombinatoricsPathwidthlawOuterplanar graphLine graphQA1-939Discrete Mathematics and CombinatoricsMathematicsMathematicsUniversal graphDistance-hereditary graph

description

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

yearjournalcountryeditionlanguage
2014-08-01Discussiones Mathematicae Graph Theory
https://doi.org/10.7151/dmgt.1745