A characterization of singular graphs

By Irene Sciriha. 2007

78 citations recorded by the source corpus.

Characterization of singular graphs can be reduced to the non-trivial solutions of a system of linear homogeneous equations Ax = 0 for the 0-1 adjacency matrix A. A graph G is singular of nullity η(G) ≥ 1, if the dimension of the nullspace ker(A) of its adjacency matrix A is η(G). Necessary and sufficient conditions are determined for a graph to be singular in terms of admissible induced subgraphs.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/ac58b12a946a7a02f5ba217bdcd408ebd3aaf409

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Gerard Jennhwa Chang
2. Hong-Gwa Yeh
3. Liang-Hao Huang

In Geometry and Topology

1. Gerard Jennhwa Chang
2. Hong-Gwa Yeh
3. Liang-Hao Huang

In Materials Chemistry

1. Gerard Jennhwa Chang
2. Hong-Gwa Yeh
3. Liang-Hao Huang

Citations in the corpus

• A characterization of graphs with rank 5 (2012, background): “The problem is very hard; only some particular results are known [5,6,12,13,16,17,23,25,26,28,29,32,33].”