Class reconstruction numbers of unicyclic graphs
نویسندگان
چکیده
منابع مشابه
Detour Index of a Class of Unicyclic Graphs
The detour index of a connected graph is defined as the sum of detour distances between all unordered pairs of vertices. We determine the n-vertex unicyclic graphs whose vertices on its unique cycle all have degree at least three with the first, the second and the third smallest and largest detour indices respectively for n ≥ 7.
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The eigenvalues of G are denoted by [Formula: see text], where n is the order of G. In particular, [Formula: see text] is called the spectral radius of G, [Formula: see text] is the least eigenvalue of G, and the spread of G is defined to be the difference between [Formula: see text] and [Formula: see text]. Let [Formula: see text] be the set of n-vertex unicyclic graphs, each of whose vertices...
متن کاملA class of unicyclic graphs determined by their Laplacian spectrum
Let Gr,p be a graph obtained from a path by adjoining a cycle Cr of length r to one end and the central vertex of a star Sp on p vertices to the other end. In this paper, it is proven that unicyclic graph Gr,p with r even is determined by its Laplacian spectrum except for n = p+4.
متن کاملThe Laplacian Spectral Radius of a Class of Unicyclic Graphs
Let C(n, k) be the set of all unicyclic graphs with n vertices and cycle length k. For anyU ∈ C(n, k),U consists of the (unique) cycle (say Ck) of length k and a certain number of trees attached to the vertices of Ck having (in total) n − k edges. If there are at most two trees attached to the vertices of Ck, where k is even, we identify in the class of unicyclic graphs those graphs whose Lapla...
متن کاملOn reverse degree distance of unicyclic graphs
The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the...
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ژورنال
عنوان ژورنال: Applicationes Mathematicae
سال: 1988
ISSN: 1233-7234,1730-6280
DOI: 10.4064/am-20-1-117-123