K. Popat

most citedSome New Results on Energy of Graphs with Self Loops

7 citations · 9 across the 6 of their papers we have counts for

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math.CO2026

Some New Results on Seidel Equienergetic Graphs

Samir K. Vaidya, Kalpesh M. Popat

The energy of a graph $G$ is the sum of the absolute values of the eigenvalues of the adjacency matrix of $G$ . Some variants of energy can also be found in the literature which are…

math.CO2026★ 7 cited

Some New Results on Energy of Graphs with Self Loops

Kalpesh M. Popat, Kunal R. Shingala

The graph $G_{σ}$ is obtained from graph $G$ by attaching self loops on $σ$ vertices. The energy $E (G_{σ})$ of the graph $G_{σ}$ with order $n$ and eigenvalues $λ_{1}, λ_{2}, \dots, λ_{n}$ is de…

math.CO2026★ 2 cited

Locally Equienergetic Graphs

Cahit Dede, Kalpesh M. Popat

For a given graph $ G $, let $ G^{(j)} $ denote the graph obtained by the deletion of vertex $ v_j $ from $ G $. The difference $ \mathscr{E}(G) - \mathscr{E}(G^{(j)}) $…

math.CO2026

Graph Energies of Generalized and Shadow-Splitting Graphs

Ronak B. Dudhat, Vinodray J. Kaneria, Kalpesh M. Popat

We extend the notions of the m-splitting graph Sm(G) and the m-shadow graph Dm(G) to introduce two new graph operations: the (p, q)-generalized splitting graph Sp,q(G) and the (c,…