GENERAL SUM CONNECTIVITY ENERGY OF GRAPH
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초록
Let G be a simple graph with vertex set V(G) = {v₁, v₂, ..., vₙ} and edge set E(G). The general sum connectivity matrix of a graph G, where each vertex vᵢ has degree dᵢ, is defined as an n × n matrix in which the (i, j)-entry is equal to (dᵢ + dⱼ)^α if the vertices vᵢ and vⱼ are adjacent, and 0 otherwise. The general sum connectivity energy is defined as the sum of the absolute values of the eigenvalues of the general sum connectivity matrix. We provide lower and upper bounds for the general sum connectivity energy (GSCE).
Abstract
Let G be a simple graph with vertex set V(G) = {v₁, v₂, ..., vₙ} and edge set E(G). The general sum connectivity matrix of a graph G, where each vertex vᵢ has degree dᵢ, is defined as an n × n matrix in which the (i, j)-entry is equal to (dᵢ + dⱼ)^α if the vertices vᵢ and vⱼ are adjacent, and 0 otherwise. The general sum connectivity energy is defined as the sum of the absolute values of the eigenvalues of the general sum connectivity matrix. We provide lower and upper bounds for the general sum connectivity energy (GSCE).
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