Two Graphs with a Common Edge

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 r...

Full description

Bibliographic Details
Main Author:	Badura Lidia
Format:	Article
Language:	English
Published:	Sciendo 2014-08-01
Series:	Discussiones Mathematicae Graph Theory
Subjects:	graph adjacency matrix determinant of graph path cycle
Online Access:	https://doi.org/10.7151/dmgt.1745

id	doaj-64f83d5d17f14fab845415f8a593ede3
record_format	Article
spelling	doaj-64f83d5d17f14fab845415f8a593ede32021-09-05T17:20:20ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922014-08-0134349750710.7151/dmgt.1745dmgt.1745Two Graphs with a Common EdgeBadura Lidia0Mathematics and Computer Science Department University of Opole Oleska 48 45-052 Opole, PolandLet 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 exampleshttps://doi.org/10.7151/dmgt.1745graphadjacency matrixdeterminant of graphpathcycle
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Badura Lidia
spellingShingle	Badura Lidia Two Graphs with a Common Edge Discussiones Mathematicae Graph Theory graph adjacency matrix determinant of graph path cycle
author_facet	Badura Lidia
author_sort	Badura Lidia
title	Two Graphs with a Common Edge
title_short	Two Graphs with a Common Edge
title_full	Two Graphs with a Common Edge
title_fullStr	Two Graphs with a Common Edge
title_full_unstemmed	Two Graphs with a Common Edge
title_sort	two graphs with a common edge
publisher	Sciendo
series	Discussiones Mathematicae Graph Theory
issn	2083-5892
publishDate	2014-08-01
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
topic	graph adjacency matrix determinant of graph path cycle
url	https://doi.org/10.7151/dmgt.1745
work_keys_str_mv	AT baduralidia twographswithacommonedge
_version_	1717786511446900736

Two Graphs with a Common Edge

Similar Items