10 papers
A Decomposition of the Hitting Time Index Using the Kirchhoff Index and an Asymmetry Term
Shunya Tamura, José Luis Palacios, Aleksandar Petojević
We study the hitting time index, a graph invariant defined in terms of expected hitting times of simple random walks on finite connected graphs, through its relation with the Kirch…
Edge-Defect Spectral Methods for Higher-Order Rankings of Spanning Tree Counts
Shunya Tamura, José Luis Palacios
In this paper, we study the higher-order ranking, by spanning-tree count, of graphs obtained from a complete graph by deleting a fixed number of edges. Using the edge-defect matrix…
Rooted spanning forests in wheel graphs: Fibonacci-Lucas formulas and extremal root configurations
Shunya Tamura, Yuuho Tanaka
In this paper, we study rooted spanning forests in the wheel graph . For a root set consisting of rim vertices, we give an explicit formula, in terms of Fibonacci and…
Edge-defect matrices and stability of the Kirchhoff index for complete graphs with deleted edges
Shunya Tamura
In this paper, we study the effective resistance, the Kirchhoff index, and the number of spanning trees of the connected graph , which is obtained from the complete graph by…
Chebyshev Recurrence Structures for Reduced Spectral Functions of Cyclic Circulant Graphs
Shunya Tamura
Let be a nonempty finite set of positive integers, let , and let , , be the normalized product sequence associated with the Chebyshev-type polynomial of…
Effective Resistance and Generalized Bejaia-Pisa Sequences on Complete Graphs with Circulant Distance Deletions
Shunya Tamura, Yuuho Tanaka
In this paper, we investigate the effective resistance on the graph , which is obtained by deleting all edges corresponding to circular distances $\{\pm1, \pm2, \dots, \…
Effective resistance and spanning trees in complete graphs with distance-class deletions
Shunya Tamura
In this paper, we consider circulant graphs obtained from the complete graph by deleting all edges belonging to a prescribed distance class. We study, in a unified manner, th…
On the average hitting times of the directed wheel
Shunya Tamura
In this paper, following the paper ``On the average hitting times of the squares of cycles,'' we provide an explicit formula for the average hitting times of a simple random walk o…
Fibonacci and Lucas numbers arising from two-component spanning forests of wheel graphs
Tsuyoshi Miezaki, Shunya Tamura
In this paper, we present a constructive bijection between a conditioned spanning forest of the wheel graph and a spanning tree of the fan graph . In addition, by ap…
Number of spanning trees in a wheel graph with two identified vertices via hitting times
Shunya Tamura, Yuuho Tanaka
In this paper, we provide an exact formula for the average hitting times in a wheel graph using a combinatorial approach. For this wheel graph, the average hitting times…