فهرست مطالب

Transactions on Combinatorics - Volume:6 Issue: 1, Mar 2017

Transactions on Combinatorics
Volume:6 Issue: 1, Mar 2017

  • تاریخ انتشار: 1395/10/15
  • تعداد عناوین: 6
|
  • Sanghita Dutta *, Chanlemki Lanong Pages 1-11
    ýThe annihilator graph AG(R) of a commutative ring R is a simple undirected graph with the vertex set Z(R)∗ and two distinct vertices are adjacent if and only if ann(x)∪ann(y) ≠ ann(xy)ý. ýIn this paper we give the sufficient condition for a graph AG(R) to be completeý. ýWe characterize rings for which AG(R) is a regular graphý, ýwe show that γ(AG(R))∈{1,2} and we also characterize the rings for which AG(R) has a cut vertexý. ýFinally we find the clique number of a finite reduced ring and characterize the rings for which AG(R)is a planar graphý.
    Keywords: ?Annihilator?, ?Clique number?, ?Domination Number
  • Yun Gao, Mohammad Reza Farahani, Wei Gao* Pages 13-19
    A graph G is called a fractionalý ý(k,n′,m)-critical deleted graph if any n′ vertices are removedý ýfrom G the resulting graph is a fractional (k,m)-deletedý ýgraphý. ýIn this paperý, ýwe prove that for integers k≥2ý, ýn′,m≥0ý, ýn≥8k′−7ý, ýand δ(G)≥k′ý, ýifý ý |NG(x)∪NG(y)|≥n′2 ý ýfor each pair of non-adjacent vertices xý, ýy of Gý, ýthen Gý ýis a fractional (k,n′,m)-critical deleted graphý. ýThe bounds forý ýneighborhood union conditioný, ýthe order n and the minimum degreeý ýδ(G) of G are all sharpý.
    Keywords: ýGraphý, ýfractionalý ýfactorý, ýfractional $(k, n', m)$, critical deleted graphý, ýneighborhoodý ýunion condition
  • Shariefuddin Pirzada, Bilal A. Chat Pages 21-27
    The set of all non-increasing non-negative integer sequences π=(d1ý,ýd2,…,dn) is denoted by NSný. ýA sequence π∈NSn is said to be graphic if it is the degree sequence of a simple graph G on n verticesý, ýand such a graph G is called a realization of πý. ýThe set of all graphic sequences in NSn is denoted by GSný. ýThe complete product split graph on LýýM vertices is denoted by S¯¯¯Lý,ýM=KL∨K¯¯¯¯¯Mý, ýwhere KL and KM are complete graphs respectively on L=∑i=1pri and M=∑i=1psi vertices with ri and si being integersý. ýAnother split graph is denoted by SLý,ýM=S¯¯¯r1ý,ýs1∨S¯¯¯r2ý,ýs2∨⋯∨S¯¯¯rpý,ýsp=(Kr1∨K¯¯¯¯¯s1)∨(Kr2∨K¯¯¯¯¯s2)∨⋯∨(Krp∨K¯¯¯¯¯sp)ý. ýA sequence π=(d1ý,ýd2,…,dn) is said to be potentially SLý,ýM-graphic (respectively S¯¯¯Lý,ýM)-graphic if there is a realization G of π containing SLý,ýM (respectively S¯¯¯Lý,ýM) as a subgraphý. ýIf π has a realization G containing SLý,ýM on those vertices having degrees d1ý,ýd2,…,dLý, ýthen π is potentially ALý,ýM-graphicý. ýA non-increasing sequence of non-negative integers π=(d1ý,ýd2,…,dn) is potentially ALý,ýM-graphic if and only if it is potentially SLý,ýM-graphicý. ýIn this paperý, ýwe obtain the sufficient condition for a graphic sequence to be potentially ALý,ýM -graphic and this result is a generalization of that given by Jý. ýHý. ýYin on split graphsý.
    Keywords: ýSplit graphý, ýcomplete product split graphý, ýpotentially H, graphic Sequences
  • Zeinab Jafari *, Mehrdad Azadi Pages 29-37
    Let R be a commutative ring with identityý. ýWe useý ýφ(R) to denote the comaximal ideal graphý. ýThe verticesý ýof φ(R) are proper ideals of R which are not containedý ýin the Jacobson radical of Rý, ýand two vertices I and J areý ýadjacent if and only if IýýJ=Rý. ýIn this paper we show someý ýproperties of this graph together with planarity of line graphý ýassociated to φ(R)ý.
    Keywords: ??Comaximal graph?, ?planar graph?, ?line? ?graph
  • Masoud Ariannejad *, Mojgan Emami, Ozra Naserian Pages 39-46
    We use the recursive method of construction large sets of t-designs given by Qiu-rong Wu (A note on extending t-designsý, ý{\em Australasý. ýJý. ýCombin.}ý, ý{\bf 4} (1991) 229--235.), and present a similar method for constructing t -subset-regularý ýself-complementary k-uniform hypergraphs of order vý. ýAs aný ýapplication we show the existence of a new family of 2-subset-regularý ýself-complementary 4-uniform hypergraphs with v=16mý.
    Keywords: Self, complementary? ?hypergraph?, ?Uniform hypergraph?, ?Regular hypergraph?, ?Large sets of t, designs
  • Gholam Hossein Fath, Tabar *, Fatemeh Taghvaee Pages 47-54
    Let G be a simple graphý, ýand Gσý ýbe an oriented graph of G with the orientation ýσ and skew-adjacency matrix S(Gσ)ý. ýThe k−th skew spectralý ýmoment of Gσý, ýdenoted byý ýTk(Gσ)ý, ýis defined as ∑ni=1(ýýýλi)ký, ýwhere λ1ý,ýλ2,⋯ý,ýλn are the eigenvalues of Gσý. ýSupposeý ýGσ11 and Gσ22 are two digraphsý. ýIf thereý ýexists an integer ký, ý1≤k≤n−1ý, ýsuch that for eachý ýiý, ý ≤i≤k−1ý, ýTi(Gσ11)=ýýTi(Gσ22) andý ýTk(Gσ11)
    Keywords: ??Oriented graph?, ?skew spectral moment?, ?skew eigenvalue?, ?T, order?, ?skew characteristic polynomial