On Two Laplacian Matrices for Skew Gain Graphs
| Autor: | K. A. Germina, Roshni T Roy, K. Shahul Hameed |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Gain graph
Multiplicative group Applied Mathematics graph adjacency matrix laplacian matrix incidence matrix graph eigenvalue skew gain graph Skew Incidence matrix Orientation (graph theory) Combinatorics QA1-939 FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics 05C22 05C50 05C76 Adjacency matrix Combinatorics (math.CO) Laplacian matrix Laplace operator Mathematics MathematicsofComputing_DISCRETEMATHEMATICS |
| Zdroj: | Electronic Journal of Graph Theory and Applications, Vol 9, Iss 1, Pp 125-135 (2021) |
| Popis: | Let $G=(V,\overrightarrow{E})$ be a graph with some prescribed orientation for the edges and $\Gamma$ be an arbitrary group. If $f\in \mathrm{Inv}(\Gamma)$ be an anti-involution then the skew gain graph $\Phi_f=(G,\Gamma,\varphi,f)$ is such that the skew gain function $\varphi:\overrightarrow{E}\rightarrow \Gamma$ satisfies $\varphi(\overrightarrow{vu})=f(\varphi(\overrightarrow{uv}))$. In this paper, we study two different types, Laplacian and $g$-Laplacian matrices for a skew gain graph where the skew gains are taken from the multiplicative group $F^\times$ of a field $F$ of characteristic zero. Defining incidence matrix, we also prove the matrix tree theorem for skew gain graphs in the case of the $g$-Laplacian matrix. Comment: 15 pages |
| Databáze: | OpenAIRE |
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