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- W4324385557 abstract "For positive integers m1,m2,…,mh, a generalized balanced tree T(m1,m2,…,mh) is a rooted tree of height h such that every vertex of depth i has mi+1 children, 0≤i≤h−1. The distance matrix D(G) of a simple connected graph G of order n is an n×n matrix whose (i,j)th entry is the distance between ith and jth vertices. A connected graph G is called a k-partitioned transmission regular graph if there exists a vertex partition {V1,V2,…,Vk} of G so that for 1≤i,j≤k, and x∈Vi, ∑y∈Vjd(x,y) is a constant. Here we show that T(m1,m2,…,mh) is an (h+1)-partitioned transmission regular graph. We find an (h+1)×(h+1) matrix whose largest eigenvalue is the distance spectral radius of T(m1,m2,…,mh). We obtain the characteristic polynomial of D(T(m1,m2,…,mh)) in terms of that of the smaller matrices and give an idea to find the full spectrum. Moreover, we get that D(T(m1,m2,…,mh)) has −2 an eigenvalue with multiplicity at least m1⋯mh−1(mh−1) and −(mh+2)±mh(mh+4) as eigenvalues with multiplicity at least m1⋯mh−2(mh−1−1)." @default.
- W4324385557 created "2023-03-16" @default.
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- W4324385557 date "2023-03-15" @default.
- W4324385557 modified "2023-09-29" @default.
- W4324385557 title "On the distance spectrum of generalized balanced trees" @default.
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- W4324385557 doi "https://doi.org/10.1080/03081087.2023.2187014" @default.
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