On the Kernel Eigenspace of Coalescence of Singular Graphs
Résumé
A finite simple undirected graph is said to be singular if its adjacency matrix has eigenvalue 0.
If a vertex u in a graph G1 is identified with a vertex v in a graph G2, then the resulting graph G1 ◦ G2, of
order |G1|+|G2|−1, is called the coalescence of G1 and G2 with respect to u and v. Singular graphs consist
of core and noncore vertices. In this paper, we coalesce two singular graphs and study the kernel eigenspace
of G1 ◦G2, and based on this analysis, determine the core and noncore vertices of the coalesced graph.
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