This article uncovers the Gourava index adjacency polynomial in regular graphs, implying new insights into graph theory.
The Gourava index adjacency polynomial of a graph G is the characteristic polynomial of the Gourava index adjacency matrix GIA(G) whose (i, j)-th entry is d(vi) + d(vj) + d(vi)d(vj), whenever the vertex vi is adjacent to vj, otherwise it is zero, where di is the degree of the vertex vi. In this article, we obtain the Gourava index adjacency polynomial of graphs obtained from regular graphs.
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Cangül et al. (2025) studied this question.
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