# Search results

Graphs and Combinatorics > 2019 > 35 > 1 > 67-89

*G*is said to be

*pancyclic*if

*G*contains cycles of lengths from 3 to |

*V*(

*G*)|. For a positive integer

*i*, we use $$Z_i$$ Z i to denote the graph obtained by identifying an endpoint of the path $$P_{i+1}$$ P i + 1 with a vertex of a triangle. In this paper, we show that every 4-connected claw-free $$Z_8$$ Z 8 -free graph is either pancyclic or is the line graph of the Petersen...

Graphs and Combinatorics > 2018 > 34 > 6 > 1691-1711

*G*of order $$n\ge 3$$ n≥3 is

*pancyclic*if

*G*contains a cycle of each possible length from 3 to

*n*, and

*vertex pancyclic*(

*edge pancyclic*) if every vertex (edge) is contained on a cycle of each possible length from 3 to

*n*. A

*chord*of a cycle is an edge between two nonadjacent vertices of the cycle, and

*chorded cycle*is a cycle containing at least one chord. We define a graph

*G*of order $$n\ge...

Information Processing Letters > 2018 > 138 > C > 7-11

The Journal of Analysis > 2019 > 27 > 2 > 555-566

*R*be a finite commutative ring with nonzero identity and

*U*(

*R*) be the set of all units of

*R*. The graph $$\Gamma =\Gamma (R,U(R),U(R))$$ Γ = Γ ( R , U ( R ) , U ( R ) ) is the simple undirected graph with vertex set

*R*in which two distinct vertices

*x*and

*y*are adjacent if and only if there exists a unit element

*u*in

*U*(

*R*) such that $$x+uy$$ x + u y is a unit in

*R*. In this paper, we...

Discussiones Mathematicae Graph Theory > 2017 > 37 > 3 > 649-663

Communications in Computer and Information Science > Informatics Engineering and Information Science > Distributed and Parallel Computing > 431-439

Graphs and Combinatorics > 2016 > 32 > 5 > 1817-1828

*G*on

*n*vertices is said to be (

*k*,

*m*)

*-pancyclic*if every set of

*k*vertices in

*G*is contained in a cycle of length

*r*for each integer

*r*in the set $$\{ m, m + 1, \ldots , n \}$$ { m , m + 1 , … , n } . This property, which generalizes the notion of a vertex pancyclic graph, was defined by Faudree et al. in (Graphs Combin 20:291–310, 2004). The notion of (

*k*,

*m*)-pancyclicity provides...

Journal of Combinatorial Optimization > 2016 > 31 > 2 > 912-917

*weakly geodesic pancyclic*...

Electronic Notes in Discrete Mathematics > 2015 > 49 > C > 181-187

Discrete Applied Mathematics > 2015 > 193 > C > 180-186

Discussiones Mathematicae Graph Theory > 2015 > 35 > 2 > 271-281

Graphs and Combinatorics > 2015 > 31 > 6 > 2149-2158

Information Sciences > 2014 > 275 > Complete > 257-266

_{n}, a variation of the hypercube, possesses some properties superior to those of the hypercube. In this paper, we show that every vertex in AQ

_{n}lies on a fault-free cycle of every length from 4 to 2

^{n}, even if there are up to 2n−3 link faults. We also show that this result is optimal.

Graphs and Combinatorics > 2014 > 30 > 1 > 1-46

Graphs and Combinatorics > 2014 > 30 > 5 > 1271-1282

*v*

_{1},

*a*

_{1},

*v*

_{2},

*a*

_{2},

*v*

_{3}, . . . ,

*v*

_{ n-1},

*a*

_{ n-1},

*v*

_{ n }in which vertex

*v*

_{ n }=

*v*

_{1}, arc

*a*

_{ i }=

*v*

_{ i }

*v*

_{ i+1}for

*i*= 1, 2, . . . ,

*n*−1, and $${a_i \neq a_j}$$ a i ≠ a j if $${i \neq j}$$ i ≠ j . In this paper, we shall show that...

Discrete Mathematics > 2013 > 313 > 20 > 2119-2123

Discrete Mathematics > 2013 > 313 > 19 > 2034-2053

Journal of Graph Theory > 74 > 3 > 260 - 274

Information Sciences > 2013 > 242 > Complete > 92-102

_{C}(x,y)=l for any integer l satisfying d

_{G}(x,y)⩽l⩽⌈∣V(G)∣/2⌉, where d

_{G}(x,y) (respectively, d

_{C}(x,y)) denotes the distance between vertices x and y in G (respectively, on C), and ∣V(G)∣ is the total number of vertices in...

Discrete Mathematics > 2013 > 313 > 4 > 460-467