IEICE TRANSACTIONS on Fundamentals
Properties of Circuits in a W-Graph
Summary :
A W-graph is a partially known graph which contains wild-components. A wild-component is an incompletely defined connected subgraph having p vertices and p-1 unspecified edges. The informations we know on a wild-component are which has a vertex set and between any two vertices there is one and only one path. In this paper, we discuss the properties of circuits in a W-graph (called W-circuits). Although a W-graph has unspecified edges, we can obtain some important properties of W-circuits. We show that the W-ring sum of W-circuits is also a W-circuit in the same W-graph. The following (1) and (2) are proved: (1) A W-circuit Ci of a W-graph can be transformed into either a circuit or an edge disjoint union of circuits, denoted by Ci*, of a graph derived from the W-graph, (2) if W-circuits C1, C2, ・・・, Cn are linearly independent, then C1*, C2*, ・・・, Cn* obtained in (1) are also linearly independent.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.10 pp.1692-1699
- Publication Date
- 1994/10/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Graphs, Networks and Matroids
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Hua-An ZHAO, Wataru MAYEDA, "Properties of Circuits in a W-Graph" in IEICE TRANSACTIONS on Fundamentals,
vol. E77-A, no. 10, pp. 1692-1699, October 1994, doi: .
Abstract: A W-graph is a partially known graph which contains wild-components. A wild-component is an incompletely defined connected subgraph having p vertices and p-1 unspecified edges. The informations we know on a wild-component are which has a vertex set and between any two vertices there is one and only one path. In this paper, we discuss the properties of circuits in a W-graph (called W-circuits). Although a W-graph has unspecified edges, we can obtain some important properties of W-circuits. We show that the W-ring sum of W-circuits is also a W-circuit in the same W-graph. The following (1) and (2) are proved: (1) A W-circuit Ci of a W-graph can be transformed into either a circuit or an edge disjoint union of circuits, denoted by Ci*, of a graph derived from the W-graph, (2) if W-circuits C1, C2, ・・・, Cn are linearly independent, then C1*, C2*, ・・・, Cn* obtained in (1) are also linearly independent.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_10_1692/_p
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@ARTICLE{e77-a_10_1692,
author={Hua-An ZHAO, Wataru MAYEDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Properties of Circuits in a W-Graph},
year={1994},
volume={E77-A},
number={10},
pages={1692-1699},
abstract={A W-graph is a partially known graph which contains wild-components. A wild-component is an incompletely defined connected subgraph having p vertices and p-1 unspecified edges. The informations we know on a wild-component are which has a vertex set and between any two vertices there is one and only one path. In this paper, we discuss the properties of circuits in a W-graph (called W-circuits). Although a W-graph has unspecified edges, we can obtain some important properties of W-circuits. We show that the W-ring sum of W-circuits is also a W-circuit in the same W-graph. The following (1) and (2) are proved: (1) A W-circuit Ci of a W-graph can be transformed into either a circuit or an edge disjoint union of circuits, denoted by Ci*, of a graph derived from the W-graph, (2) if W-circuits C1, C2, ・・・, Cn are linearly independent, then C1*, C2*, ・・・, Cn* obtained in (1) are also linearly independent.},
keywords={},
doi={},
ISSN={},
month={October},}
Copy
TY - JOUR
TI - Properties of Circuits in a W-Graph
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1692
EP - 1699
AU - Hua-An ZHAO
AU - Wataru MAYEDA
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 1994
AB - A W-graph is a partially known graph which contains wild-components. A wild-component is an incompletely defined connected subgraph having p vertices and p-1 unspecified edges. The informations we know on a wild-component are which has a vertex set and between any two vertices there is one and only one path. In this paper, we discuss the properties of circuits in a W-graph (called W-circuits). Although a W-graph has unspecified edges, we can obtain some important properties of W-circuits. We show that the W-ring sum of W-circuits is also a W-circuit in the same W-graph. The following (1) and (2) are proved: (1) A W-circuit Ci of a W-graph can be transformed into either a circuit or an edge disjoint union of circuits, denoted by Ci*, of a graph derived from the W-graph, (2) if W-circuits C1, C2, ・・・, Cn are linearly independent, then C1*, C2*, ・・・, Cn* obtained in (1) are also linearly independent.
ER -
English
