Abstract
Study of any graph class includes characterization, recognition, counting the number of graphs i.e. cataloging and construction of graphs. The construction of sc chordal graphs by mean of complementing permutation is one of the known method. In this paper, a new method for the construction of sc chordal graphs is proposed based on a two-pair of graphs. We also presented algorithm for the construction of sc weakly chordal graphs.
Highlights
Let G = (V, E) be an undirected graph with no loops or multiple edges where V(G) and E(G) denote the set of vertices and edges of G respectively
Let S ⊆ V(G) be a set of vertices of G; the subgraph of G induced by S is denoted by G [S]
The degree sequence of a graph G is the sequence of the degrees of the n vertices of G arranged in non-increasing order and is denoted by d1 ≥ d2 ≥ ... ≥ dn
Summary
Let G = (V, E) be an undirected graph with no loops or multiple edges where V(G) and E(G) denote the set of vertices and edges of G respectively. A graph is self-complementary (sc) if it is isomorphic to its complement. A graph G is chordal if it has no chordless cycle of length greater than or equal to 4 and it is weakly chordal if both G and its complement G have no chordless cycle of length greater than or equal to 5. Huang gave a method to construct many classes of connected graphs with exactly kmain eigenvalues for any positive integer k.
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