Hamiltonicity of the Complete Double Vertex Graph of some Join Graphs
نویسندگان
چکیده
The complete double vertex graph $M_2(G)$ of $G$ is defined as the whose vertices are $2$-multisubsets $V(G)$, and two such adjacent in if their symmetric difference (as multisets) a pair $G$. In this paper we exhibit an infinite family graphs (containing Hamiltonian non-Hamiltonian graphs) for which Hamiltonian.
منابع مشابه
The automorphism group of the reduced complete-empty $X-$join of graphs
Suppose $X$ is a simple graph. The $X-$join $Gamma$ of a set ofcomplete or empty graphs ${X_x }_{x in V(X)}$ is a simple graph with the following vertex and edge sets:begin{eqnarray*}V(Gamma) &=& {(x,y) | x in V(X) & y inV(X_x) },\ E(Gamma) &=& {(x,y)(x^prime,y^prime) | xx^prime in E(X) or else x = x^prime & yy^prime in E(X_x)}.end{eqnarray*}The $X-$join graph $Gamma$ is said to be re...
متن کاملTotal vertex irregularity strength of corona product of some graphs
A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the to...
متن کاملVertex Equitable Labeling of Double Alternate Snake Graphs
Let G be a graph with p vertices and q edges and A = {0, 1, 2, . . . , [q/2]}. A vertex labeling f : V (G) → A induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. For a ∈ A, let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |vf (a) − vf (b)| ≤ 1 and the indu...
متن کاملThe locating chromatic number of the join of graphs
Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Pi$ is defined to be the ordered $k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$, where $d(v,V_i)=min{d(v,x):~xin V_i}, 1leq ileq k$. If distinct...
متن کاملOn vertex balance index set of some graphs
Let Z2 = {0, 1} and G = (V ,E) be a graph. A labeling f : V → Z2 induces an edge labeling f* : E →Z2 defined by f*(uv) = f(u).f (v). For i ε Z2 let vf (i) = v(i) = card{v ε V : f(v) = i} and ef (i) = e(i) = {e ε E : f*(e) = i}. A labeling f is said to be Vertex-friendly if | v(0) − v(1) |≤ 1. The vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. In this paper ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Matemática Contemporânea
سال: 2022
ISSN: ['0103-9059', '2317-6636']
DOI: https://doi.org/10.21711/231766362021/rmc4815