This study aims to explore and identify the objects of architecture and ornaments Masjid Agung Kediri. In this study, the researcher used qualitative research with an ethnography approach. The instrument of this research is human instruments. The researcher is a primary instrument. As qualitative research with an ethnographic approach, the instrument of this study is the human instrument, the researcher as a primary instrument that can not be changed to someone else. The result of this research indicates that the shape, architecture, and ornaments Masjid Agung Kediri have ethnomathematics connecting with graph concept, such as mosque pillars contains line graph concept denoted by 𝑃 , prominent buttress contain cycle graph concept denoted by 𝐶 , ceiling contains cycle graph concept denoted by 𝐶 , ornaments contain wheel graph concept denoted by 𝑊 , decorative lights with three levels contain star graph concept in the first level denoted by 𝑆 , the second level denoted by 𝑆 , and the third level denoted by 𝑆 .

Let G = (V(G),E(G)) is a connected simple graph. Let ec(v) is the eccentricity of vertex v, D(v) = Σ u∈V(G) d(u,v) is the sum of all distances from vertex v and deg(v) is the degree of vertex v in G. The eccentric distance sum index of G is defined as ξd (G) = Σ v∈V(G) ec(v)D(v) and the adjacent eccentric distance sum index of G is defined as ξ s v ( G ) = ∑ v ∈ V ( G ) e c ( v ) D ( v ) deg ( v ) . For positive integer m and m ≥ 3, let D 2m be dihedral group of order 2m and N is a normal subgroup of D 2m . The subgroup graph Γ N (D 2m ) of dihedral group D 2m is a simple graph with vertex set D 2m and two distinct vertices x and y are adjacent if and only if xy ∈ N. In the present paper, we compute eccentric distance sum and adjacent eccentric distance sum index of complement of subgroup graph of dihedral group D 2m . Total eccentricity, eccentric connectivity index, first Zagreb index, and second Zagreb index of these graphs are also determined.

No abstract