We present a reduction between subgraph isomorphism and minimal partial subgraph isomorphism. We also provide a new reduction between graph isomorphism and minimal partial graph isomorphism. The new reduction is more efficient and simpler than the previous reduction and can be generalized to subgraph isomorphism. In addition, we show that a reduction from graph isomorphism that makes only one c...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set...

A graph is said to be symmetric if its automorphism group is transitive on its arcs. A complete classification is given of pentavalent symmetric graphs of order 24p for each prime p. It is shown that a connected pentavalent symmetric graph of order 24p exists if and only if p=2, 3, 5, 11 or 17, and up to isomorphism, there are only eleven such graphs.

Graph isomorphism problem is to determine whether two given graphs are isomorphic. It is a particular type of a more general problem “the isomorphism of incidence system”. I propose some new invariants for heuristic search of graph isomorphism and demonstrate that they are really useful in practice by experiments. Keyword. graph isomorphism, graph invariant, graph spectrum , adjacency matrix, m...

It has been known that the graph isomorphism problem is polynomial-time many-one reducible to the ring isomorphism problem. In fact, two different reductions have already been proposed. For those reductions, rings of certain types have been used to represent a given graph. In this paper, we give yet another reduction, which is based on a simpler and more natural construction of a ring from a gr...

The expectative sub-graph isomorphism of uncertain attribute graph is based on the analysis of complex network structure and the characteristic of uncertain attribute graph. The expectative sub-graph isomorphism of uncertain attribute graph is only one threshold value as constraint conditions. The method is simple, but the computation is large amount. Therefore, this paper brings in the definit...