Energy of a digraph with respect to a VDB topological index

نویسندگان

چکیده

Abstract Let D D be a digraph with vertex set V V and arc E E . For u u , the out-degree in-degree of are denoted by d + {d}_{u}^{+} − {d}_{u}^{-} respectively. A vertex-degree-based (VDB) topological index φ \varphi is defined for as xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> ( stretchy="false">) = 1 2 ∑ v ∈ , (D)=\frac{1}{2}\sum _{uv\in E}{\varphi }_{{d}_{u}^{+},{d}_{v}^{-}}, where i j {\varphi }_{i,j} an appropriate function which satisfies }_{i,j}={\varphi }_{j,i} In this work, we introduce energy ℰ {{\mathcal{ {\mathcal E} }}}_{\varphi }(D) respect to general VDB after comparing it underlying graph its splitting digraph, derive upper lower bounds } characterize digraphs attain these bounds.

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ژورنال

عنوان ژورنال: Special Matrices

سال: 2022

ISSN: ['2300-7451']

DOI: https://doi.org/10.1515/spma-2022-0171